SAT Prep: Test 7 Section 2 Part 3

WEBVTT
Kind: captions
Language: en

00:00:01.080 --> 00:00:04.250
We're on problem 13.

00:00:04.250 --> 00:00:07.140
A company sells boxes of
balloons in which the balloons

00:00:07.140 --> 00:00:09.260
are red, green, or blue.

00:00:09.260 --> 00:00:12.030
Luann purchased-- that
doesn't sound like a

00:00:12.030 --> 00:00:13.020
name related to me.

00:00:13.020 --> 00:00:16.090
Luann purchased a box of
balloons in which 1/3

00:00:16.090 --> 00:00:17.340
of them were red.

00:00:20.670 --> 00:00:24.250
If there were 1/2 as many green
balloons in the box as

00:00:24.250 --> 00:00:29.190
red ones-- so green is
equal to 1/2 red.

00:00:29.190 --> 00:00:30.250
Fair enough.

00:00:30.250 --> 00:00:32.332
Green is equal to 1/2 red.

00:00:32.332 --> 00:00:34.380
There's 1/2 as many green
balloons in the box as red

00:00:34.380 --> 00:00:43.350
ones, and 18 balloons were blue,
how many balloons were

00:00:43.350 --> 00:00:44.600
in the box?

00:00:47.140 --> 00:00:48.550
OK, so this is fascinating.

00:00:48.550 --> 00:00:52.120
So 1/3 are red.

00:00:52.120 --> 00:00:55.050
And then the green is 1/2 as
many as the red, right?

00:00:55.050 --> 00:00:58.370
So if 1/3 of them are red, how
may are going to be green?

00:00:58.370 --> 00:01:00.270
Well, 1/2 of the 1/3, right?

00:01:00.270 --> 00:01:07.080
So we know that 1/6 are
going to be green.

00:01:07.080 --> 00:01:08.330
How did I get 1/6?

00:01:10.500 --> 00:01:12.860
Let's say there's
10 red, right?

00:01:12.860 --> 00:01:15.950
And 10 is 1/3, then there's
going to be-- let's say

00:01:15.950 --> 00:01:17.280
there's 30 balloons.

00:01:17.280 --> 00:01:19.400
1/3 is red, so then it's 10.

00:01:19.400 --> 00:01:22.500
So green's going to be 1/2 of
that, so it'd be 5/30 or 1/6.

00:01:22.500 --> 00:01:25.710
So whatever the number is,
1/3 are red, 1/2 of

00:01:25.710 --> 00:01:27.350
that, or 1/6, are green.

00:01:27.350 --> 00:01:29.180
And there are 18 blue.

00:01:29.180 --> 00:01:30.290
So what can we do now?

00:01:30.290 --> 00:01:31.480
Well, let's figure
out what fraction

00:01:31.480 --> 00:01:33.020
would have to be blue.

00:01:33.020 --> 00:01:35.630
We know that 1/3 are
red 1/6 are green.

00:01:35.630 --> 00:01:36.760
What's left over?

00:01:36.760 --> 00:01:41.110
So what's 1 minus
1/3 minus 1/6?

00:01:41.110 --> 00:01:44.480
This will tell us how many blue,
what fraction of the

00:01:44.480 --> 00:01:45.870
balloons have to be blue.

00:01:45.870 --> 00:01:49.860
So that equals-- let's make 6
the common denominator, right?

00:01:49.860 --> 00:01:53.020
1 is equal to 6/6 minus 1/3.

00:01:53.020 --> 00:01:56.180
That's equal to 2/6 minus 1/6.

00:01:56.180 --> 00:02:00.170
So that's 6 minus 2 minus 1.

00:02:00.170 --> 00:02:03.130
So that's 3/6 are blue, right?

00:02:03.130 --> 00:02:05.010
And I just subtracted the
fraction that are red and I

00:02:05.010 --> 00:02:08.240
subtracted the fraction that
are green from the whole.

00:02:08.240 --> 00:02:13.020
And so I get 3/6, or
1/2, are blue.

00:02:13.020 --> 00:02:15.070
So 1/2 of the balloons in
the container, or in

00:02:15.070 --> 00:02:16.430
the box, are blue.

00:02:16.430 --> 00:02:19.300
And they want to know how many
balloons are in the box?

00:02:19.300 --> 00:02:21.950
Well, there are 18 blue, and
that's 1/2 of all of the

00:02:21.950 --> 00:02:23.270
balloons, right?

00:02:23.270 --> 00:02:28.520
So 18 is equal to 1/2 of
all of the balloons.

00:02:28.520 --> 00:02:31.380
Multiply both sides by 2, you
get 36 is equal to x.

00:02:31.380 --> 00:02:32.410
And you know that.

00:02:32.410 --> 00:02:34.570
18 is 1/2 of something,
then the total number

00:02:34.570 --> 00:02:36.000
of balloons is 36.

00:02:36.000 --> 00:02:36.810
That's our answer.

00:02:36.810 --> 00:02:45.710
Next problem, 14.

00:02:45.710 --> 00:02:51.460
The three distinct points P,
Q, and R lie on line L, OK?

00:02:51.460 --> 00:02:54.080
The four distinct points S, T,
U, V lie on a different line

00:02:54.080 --> 00:02:55.360
that is parallel to L.

00:02:55.360 --> 00:02:57.080
What is the total number of
different lines that can be

00:02:57.080 --> 00:03:03.610
drawn so that each line contains
exactly two of the

00:03:03.610 --> 00:03:04.860
seven points.

00:03:07.500 --> 00:03:09.060
OK, I see what they're saying.

00:03:09.060 --> 00:03:11.330
So let's draw the first
line, P, Q, and R.

00:03:14.770 --> 00:03:21.560
So let me just draw the two
lines first. So the first line

00:03:21.560 --> 00:03:23.150
is line P, Q, and R.

00:03:28.860 --> 00:03:31.735
And then the second line
is S, T, U, and V.

00:03:31.735 --> 00:03:38.080
So then we have S,
T, U, and V.

00:03:38.080 --> 00:03:40.640
And this line is parallel
to this line, right?

00:03:40.640 --> 00:03:42.540
They're parallel, so they're
never going to

00:03:42.540 --> 00:03:44.420
intersect each other.

00:03:44.420 --> 00:03:47.170
OK, what is the total number of
different lines that can be

00:03:47.170 --> 00:03:50.040
drawn so that each line
intersects exactly two of the

00:03:50.040 --> 00:03:50.710
seven points?

00:03:50.710 --> 00:03:54.300
So you can't even intersect
three of this.

00:03:54.300 --> 00:03:57.950
Well, you can, only if you
go through that line.

00:03:57.950 --> 00:03:59.860
So what is the total number of
different lines that can be

00:03:59.860 --> 00:04:06.520
drawn so that each line contains
exactly two of the

00:04:06.520 --> 00:04:06.800
seven points?

00:04:06.800 --> 00:04:07.390
Right.

00:04:07.390 --> 00:04:08.020
So that's interesting.

00:04:08.020 --> 00:04:09.670
So you can't count these
lines, right?

00:04:09.670 --> 00:04:11.030
Because these lines
have three.

00:04:11.030 --> 00:04:13.590
This line has three of the seven
points, and this line

00:04:13.590 --> 00:04:15.040
has four of the seven points.

00:04:15.040 --> 00:04:17.160
So those can't be it, because
it says exactly two.

00:04:17.160 --> 00:04:19.000
You can't have even three
of the points.

00:04:19.000 --> 00:04:19.920
Sp what are they?

00:04:19.920 --> 00:04:26.260
Well, P can go to four
points, right?

00:04:26.260 --> 00:04:28.890
I mean, I could just
count them out.

00:04:28.890 --> 00:04:33.310
P can go to four points, Q can
be connected with four points,

00:04:33.310 --> 00:04:35.360
and R can be connected
with four points, so

00:04:35.360 --> 00:04:36.120
it should be 12.

00:04:36.120 --> 00:04:37.750
And if you don't know what
I'm saying, let me

00:04:37.750 --> 00:04:39.230
just draw it out.

00:04:39.230 --> 00:04:43.380
P could be this line,
one, two.

00:04:43.380 --> 00:04:46.160
Sorry, that one wasn't
drawn well.

00:04:46.160 --> 00:04:53.400
One, two, three, four.

00:04:53.400 --> 00:05:03.300
One, two, three, four, and
then one, two, three.

00:05:03.300 --> 00:05:05.240
Well, that's kind of a
nice-looking shape there.

00:05:05.240 --> 00:05:09.540
So 4 plus 4 plus 4 is 12, so
there's 12 possible lines that

00:05:09.540 --> 00:05:12.880
intersect exactly two of
these seven points.

00:05:12.880 --> 00:05:19.585
Next problem, problem 15.

00:05:19.585 --> 00:05:21.430
I'm still using the line tool.

00:05:21.430 --> 00:05:23.260
OK, problem 15.

00:05:23.260 --> 00:05:31.150
If 2 to the x plus 2 to the x
plus 2 to the x plus-- how

00:05:31.150 --> 00:05:31.990
many of these are there?

00:05:31.990 --> 00:05:35.090
There's four of them-- plus 2
to the x is equal to 2 the

00:05:35.090 --> 00:05:39.400
seventh, what is
the value of x?

00:05:39.400 --> 00:05:40.790
So how many of these
are there?

00:05:40.790 --> 00:05:43.210
There's one, two, three, four,
which I had to figure out

00:05:43.210 --> 00:05:44.720
while I was drawing it.

00:05:44.720 --> 00:05:46.430
So there's four.

00:05:46.430 --> 00:05:48.990
We're essentially adding to the
x four times, so this is

00:05:48.990 --> 00:05:53.520
the same thing as saying 4
times 2 to the x, right?

00:05:53.520 --> 00:05:55.540
Because we have 2 to
the x four times:

00:05:55.540 --> 00:05:56.720
one, two, three, four.

00:05:56.720 --> 00:05:59.450
So this is the same thing as
this: 4 times 2 to the x.

00:05:59.450 --> 00:06:03.490
And that equals 2
to the seventh.

00:06:03.490 --> 00:06:07.460
What's 4 written as base 2?

00:06:07.460 --> 00:06:09.740
That's the same thing
as 2 squared, right?

00:06:09.740 --> 00:06:11.063
Whenever you see these problems
and you have two

00:06:11.063 --> 00:06:13.310
different bases, try to see if
you can convert them all to

00:06:13.310 --> 00:06:13.730
the same base.

00:06:13.730 --> 00:06:17.810
So that's 2 squared plus-- 2
squared times 2 to the x is

00:06:17.810 --> 00:06:19.930
equal to 2 to the seventh.

00:06:19.930 --> 00:06:22.380
2 squared times 2 to the x,
that's the same thing as 2 to

00:06:22.380 --> 00:06:24.850
the x plus 2.

00:06:24.850 --> 00:06:27.230
That equals 2 to the seventh.

00:06:27.230 --> 00:06:29.660
So x plus 2 must equal 7.

00:06:29.660 --> 00:06:31.600
x plus 2 is equal to 7.

00:06:31.600 --> 00:06:33.190
x is equal to 5.

00:06:33.190 --> 00:06:34.440
And we are done.

00:06:34.440 --> 00:06:43.030
Next problem, problem 16.

00:06:43.030 --> 00:06:46.560
Each of five people had a blank
card on which they wrote

00:06:46.560 --> 00:06:48.280
a positive integer.

00:06:48.280 --> 00:06:52.350
If the average of these integers
is 15, what is the

00:06:52.350 --> 00:06:53.990
greatest possible integers
that can be

00:06:53.990 --> 00:06:56.260
on one of the cards?

00:06:56.260 --> 00:06:57.720
This is fascinating.

00:06:57.720 --> 00:07:02.930
So essentially, they're saying
you have five positive

00:07:02.930 --> 00:07:05.310
integers and their
average is 15.

00:07:05.310 --> 00:07:07.450
What is the greatest possible
integer that could be among

00:07:07.450 --> 00:07:09.780
these cards?

00:07:09.780 --> 00:07:13.500
So think of it this way: the
sum of the five integers is

00:07:13.500 --> 00:07:14.760
going to be what?

00:07:14.760 --> 00:07:19.340
So let's say it's x1
plus x2 plus x3

00:07:19.340 --> 00:07:23.090
plus x4 plus x5, right?

00:07:23.090 --> 00:07:27.470
All of them over 5 is
equal to 15, right?

00:07:27.470 --> 00:07:29.060
That's what they told us.

00:07:29.060 --> 00:07:33.940
The average of the t numbers is
15, so the sum x1 plus x2

00:07:33.940 --> 00:07:37.960
plus x3 plus x4 plus x5
is equal to what?

00:07:37.960 --> 00:07:40.940
5 times 15, that's 75.

00:07:40.940 --> 00:07:43.640
5 times 10 is 50 plus--
OK, that's 75.

00:07:43.640 --> 00:07:46.620
So the sum of the integers
are going to be 75.

00:07:46.620 --> 00:07:51.510
And so we want to know what the
largest one of these, the

00:07:51.510 --> 00:07:52.900
greatest possible
integer here.

00:07:52.900 --> 00:07:54.540
So let's just say that
this is what we're

00:07:54.540 --> 00:07:55.240
trying to figure out.

00:07:55.240 --> 00:07:58.530
Let's try to maximize this
number here, x5.

00:07:58.530 --> 00:08:01.670
If we want this number to be
as large as possible, these

00:08:01.670 --> 00:08:05.080
numbers have to be as small
as possible, right?

00:08:05.080 --> 00:08:07.430
And you could subtract these
numbers from the other side.

00:08:07.430 --> 00:08:14.770
You could say x5 is equal to 75
minus x1 minus x2 minus x3

00:08:14.770 --> 00:08:16.720
minus x4, right?

00:08:16.720 --> 00:08:18.970
And we're going to try to
maximize this number.

00:08:18.970 --> 00:08:19.880
And then we're going to say
that's going to be the

00:08:19.880 --> 00:08:21.160
largest.

00:08:21.160 --> 00:08:23.280
So if this is the largest, we
want to subtract as small a

00:08:23.280 --> 00:08:24.950
number as possible
here, here, here.

00:08:24.950 --> 00:08:26.420
And what are the constraints?

00:08:26.420 --> 00:08:29.860
They have to be positive
integers.

00:08:29.860 --> 00:08:32.510
So each of these numbers have
to be greater than zero and

00:08:32.510 --> 00:08:33.320
have to be integers.

00:08:33.320 --> 00:08:35.430
So we want them to be as
small as possible, so

00:08:35.430 --> 00:08:36.710
let's make them 1.

00:08:36.710 --> 00:08:41.780
So let's say it's 75 minus 1
minus 1 minus 1 minus 1.

00:08:41.780 --> 00:08:45.350
That's 75 minus 4,
which equals 71.

00:08:45.350 --> 00:08:47.730
So that's the greatest
possible value

00:08:47.730 --> 00:08:50.240
of one of the integers.

00:08:50.240 --> 00:08:53.320
And I have a minute left and do
problems. No, I'd better do

00:08:53.320 --> 00:08:54.350
it in another video.

00:08:54.350 --> 00:08:56.300
So I'll see you in
the next video.


SAT Prep: Test 7 Section 2 Part 4

WEBVTT
Kind: captions
Language: en

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We are on problem 17.

00:00:05.820 --> 00:00:08.290
Alice and Corinne stand
back-to-back.

00:00:08.290 --> 00:00:11.620
They each take 10 steps in
opposite directions away from

00:00:11.620 --> 00:00:13.060
each other and stop.

00:00:13.060 --> 00:00:15.740
Alison turns around walks
towards Corinne and reaches

00:00:15.740 --> 00:00:17.090
her in 17 steps.

00:00:17.090 --> 00:00:19.720
OK, so this is interesting.

00:00:19.720 --> 00:00:23.300
So they're back-to-back.

00:00:23.300 --> 00:00:24.775
Let's say Alice goes this way.

00:00:24.775 --> 00:00:27.130
And let's say A is
for Alice steps.

00:00:27.130 --> 00:00:33.740
So 10 Alice steps, we don't know
how long Alice steps are.

00:00:33.740 --> 00:00:38.540
And then Corinne had gone this
way and taken 10 Corinne

00:00:38.540 --> 00:00:39.520
steps, right?

00:00:39.520 --> 00:00:41.930
C is, I don't know how long she
takes per step, two feet?

00:00:41.930 --> 00:00:42.970
Who knows?

00:00:42.970 --> 00:00:45.850
But C is the distance of Corinne
steps in my little

00:00:45.850 --> 00:00:47.410
world right here.

00:00:47.410 --> 00:00:49.700
OK, so they took ten steps in
opposite directions from each

00:00:49.700 --> 00:00:50.240
other and stopped.

00:00:50.240 --> 00:00:52.730
Alison turns around and walks
towards Corinne and reaches

00:00:52.730 --> 00:00:53.990
her in 17 steps.

00:00:53.990 --> 00:00:56.030
So this is where Corinne
is now, right?

00:00:56.030 --> 00:01:07.380
So this whole distance here
is 17 Alice steps.

00:01:07.380 --> 00:01:11.010
The length of one of Alice steps
is how many times the

00:01:11.010 --> 00:01:12.920
length of one of Corinne's
steps?

00:01:12.920 --> 00:01:15.580
And they say, all of Alice's
steps are the same length, and

00:01:15.580 --> 00:01:17.990
all of Corinne's steps
are the same length.

00:01:17.990 --> 00:01:19.390
Well we know a couple
of things.

00:01:19.390 --> 00:01:22.680
We know to get to here
would have been 10

00:01:22.680 --> 00:01:23.920
Alice steps, right?

00:01:23.920 --> 00:01:26.790
This would have been
10 Alice steps.

00:01:26.790 --> 00:01:30.370
So essentially, in the same
distance that Corinne took 10

00:01:30.370 --> 00:01:32.090
steps, Alice took what?

00:01:32.090 --> 00:01:34.330
She took 7 steps, right?

00:01:34.330 --> 00:01:36.500
She took 10 to get to the
middle, and then 7 more to get

00:01:36.500 --> 00:01:37.476
to where Corinne is.

00:01:37.476 --> 00:01:39.870
So this is 7 Alice steps.

00:01:39.870 --> 00:01:44.470
So 7 times Alice step length is
equal to 10 times Corinne

00:01:44.470 --> 00:01:45.830
step length, right?

00:01:45.830 --> 00:01:47.610
I'm just saying 7a
is equal to 10c.

00:01:47.610 --> 00:01:48.740
And what do we want to know?

00:01:48.740 --> 00:01:52.280
We want to know the length of
one of Alice's steps is how

00:01:52.280 --> 00:01:53.840
many times the length of
one of Corinne's steps?

00:01:53.840 --> 00:01:54.770
So we want to solve for a.

00:01:54.770 --> 00:01:57.786
So Alice's step is equal to--
divide both sides by 7-- is

00:01:57.786 --> 00:02:01.520
equal to 10/7 times
a Corinne step.

00:02:01.520 --> 00:02:04.460
And that's our answer, 10/7.

00:02:04.460 --> 00:02:13.230
Next problem, problem 18.

00:02:13.230 --> 00:02:20.390
Let the function f be defined
by f of x is equal to x

00:02:20.390 --> 00:02:24.950
squared plus 18.

00:02:24.950 --> 00:02:33.710
If m is a positive number such
that f of 2m is equal to 2 f

00:02:33.710 --> 00:02:37.960
of m, what is the value of m?

00:02:37.960 --> 00:02:39.360
A lot of people get intimidated
by these function

00:02:39.360 --> 00:02:40.780
problems, but in some ways
they're kind of the most

00:02:40.780 --> 00:02:42.490
straightforward problems.
You just have to sit

00:02:42.490 --> 00:02:43.670
and evaluate them.

00:02:43.670 --> 00:02:45.250
So what's f of 2m?

00:02:45.250 --> 00:02:47.670
So everywhere we see
an x, we put a 2m.

00:02:47.670 --> 00:02:53.730
So it's 2m squared
plus 18, right?

00:02:53.730 --> 00:02:55.115
Wherever I saw an
x, I put a 2m.

00:02:55.115 --> 00:02:58.475
And that equals 2
times f of m.

00:02:58.475 --> 00:03:00.200
So wherever I see an
x, I put an m.

00:03:00.200 --> 00:03:05.360
So that's m squared plus 18.

00:03:05.360 --> 00:03:06.870
Now I just simplify.

00:03:06.870 --> 00:03:14.510
2m squared, that's equal to 4m
squared plus 18 is equal to 2m

00:03:14.510 --> 00:03:16.680
squared plus 36.

00:03:16.680 --> 00:03:18.760
I just distributed the 2.

00:03:18.760 --> 00:03:22.100
So you subtract 2m squared from
both sides, you get 2m

00:03:22.100 --> 00:03:24.870
squared plus 18 is
equal to 36.

00:03:24.870 --> 00:03:27.060
I subtracted this
from both sides.

00:03:27.060 --> 00:03:29.590
Subtract 18 from both
sides, you get 2m

00:03:29.590 --> 00:03:32.090
squared is equal to 18.

00:03:32.090 --> 00:03:38.110
Divide both sides by 2, you get
m squared is equal to 9.

00:03:38.110 --> 00:03:43.180
And then you get m is equal
to-- if you just did this

00:03:43.180 --> 00:03:44.850
straight off, you'd get
plus or minus 3.

00:03:44.850 --> 00:03:46.920
But they tell us that m is a
positive number, so we know

00:03:46.920 --> 00:03:48.780
that m is equal to 3.

00:03:48.780 --> 00:03:50.162
And we are done.

00:03:50.162 --> 00:03:51.280
And that's it.

00:03:51.280 --> 00:03:54.440
I'll see you in the
next section.


SAT Prep: Test 6 Section 9 Part 1

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:03.490
We're in the last section
of test 6.

00:00:03.490 --> 00:00:06.170
Section 9, page 743.

00:00:06.170 --> 00:00:09.660
Problem number 1.

00:00:09.660 --> 00:00:12.900
For which of the following
values of m will the value of

00:00:12.900 --> 00:00:20.130
3m minus 1 be greater than 10?

00:00:20.130 --> 00:00:22.570
So we add 1 to both sides.

00:00:22.570 --> 00:00:26.960
3m is going to be
greater than 11.

00:00:26.960 --> 00:00:29.050
Divide both sides by 3, and you
don't have to switch the

00:00:29.050 --> 00:00:30.530
inequality because
3 is positive.

00:00:30.530 --> 00:00:34.650
So you get m is going to
be greater than 11/3.

00:00:34.650 --> 00:00:36.580
And 11/3, this is what?

00:00:36.580 --> 00:00:39.480
This is equal to 3 and 2/3.

00:00:39.480 --> 00:00:41.880
So anything greater than
3, really, any integer

00:00:41.880 --> 00:00:42.790
greater than 3.

00:00:42.790 --> 00:00:44.310
If you look at all the choices,
the only one that's

00:00:44.310 --> 00:00:50.040
greater than 3 and 2/3
is choice A, 4.

00:00:50.040 --> 00:00:52.620
Next problem.

00:00:52.620 --> 00:00:58.650
If a times k is equal to k--
sorry, if a times k is equal

00:00:58.650 --> 00:01:05.050
to a for all values of a,
what is the value of k?

00:01:05.050 --> 00:01:06.590
And the reason why they have
to say all values of a is

00:01:06.590 --> 00:01:09.890
because if a was 0, then that
would work for any k.

00:01:09.890 --> 00:01:12.230
But if it's for all values of
k, you divide both sides of

00:01:12.230 --> 00:01:17.110
this equation by a, you
get k is equal to a/a

00:01:17.110 --> 00:01:18.840
which is equal to 1.

00:01:18.840 --> 00:01:21.790
So k would have be equal
to 1, which is D.

00:01:21.790 --> 00:01:22.430
And you knew that.

00:01:22.430 --> 00:01:23.790
You didn't have to
do any algebra.

00:01:23.790 --> 00:01:26.980
If I multiply something times
some number and I get the

00:01:26.980 --> 00:01:30.470
original thing, that number's
going to be 1.

00:01:30.470 --> 00:01:31.720
Problem 3.

00:01:34.814 --> 00:01:36.064
Image.

00:01:39.980 --> 00:01:42.370
So let me draw what
they've drawn.

00:01:42.370 --> 00:01:45.400
So I have one parallel
line like that.

00:01:45.400 --> 00:01:47.310
I'm assuming they're parallel,
because they look parallel in

00:01:47.310 --> 00:01:50.060
the picture.

00:01:50.060 --> 00:01:54.510
And then there's a line that
comes down like this.

00:01:54.510 --> 00:01:57.266
There's another line that
goes up like that.

00:01:57.266 --> 00:01:59.580
And what do they tell
us about it?

00:01:59.580 --> 00:02:03.280
They tell us that this is
x degrees right here.

00:02:03.280 --> 00:02:06.870
This is z degrees.

00:02:06.870 --> 00:02:08.330
This is y degrees.

00:02:08.330 --> 00:02:09.389
This is line l.

00:02:09.389 --> 00:02:11.500
This is line m.

00:02:11.500 --> 00:02:13.795
In the figure above,
l is parallel to m.

00:02:17.390 --> 00:02:22.655
If x is equal to 80 degrees-- so
this is 80 degrees-- and y

00:02:22.655 --> 00:02:29.850
is equal to 70 degrees, what
is the value of z?

00:02:29.850 --> 00:02:32.860
So the trick here is just to
see the opposite angles.

00:02:32.860 --> 00:02:35.800
In fact, the information that
they're parallel lines is

00:02:35.800 --> 00:02:37.970
actually just extra information
to start making

00:02:37.970 --> 00:02:39.870
you do corresponding
angles and all that

00:02:39.870 --> 00:02:40.850
kind of fancy stuff.

00:02:40.850 --> 00:02:42.380
Which you could do.

00:02:42.380 --> 00:02:44.950
But the really easy thing is to
realize that x, this angle,

00:02:44.950 --> 00:02:47.020
is the same thing as this
angle, which is

00:02:47.020 --> 00:02:49.130
going to be 80 degrees.

00:02:49.130 --> 00:02:49.400
Right?

00:02:49.400 --> 00:02:52.090
Because they're opposite angles
of intersecting lines.

00:02:52.090 --> 00:02:54.170
And this-- if that's 70,
then this angle is

00:02:54.170 --> 00:02:56.260
also going to be 70.

00:02:56.260 --> 00:02:59.840
And now 80 plus 70 plus z has to
equal 180, because they're

00:02:59.840 --> 00:03:02.095
all in the same triangle
together.

00:03:02.095 --> 00:03:07.920
So 80 plus 70 plus z
is equal to 180.

00:03:07.920 --> 00:03:11.660
150 plus z is equal to 180.

00:03:11.660 --> 00:03:14.750
Subtract 150 from both
sides, you get z

00:03:14.750 --> 00:03:17.260
is equal to 30 degrees.

00:03:17.260 --> 00:03:20.080
The other way you could have
done it is you could have used

00:03:20.080 --> 00:03:21.990
the information about
the parallel lines.

00:03:21.990 --> 00:03:24.350
And you could have said, well,
the corresponding angle here

00:03:24.350 --> 00:03:26.360
is here, so that this
is also 80 degrees.

00:03:26.360 --> 00:03:27.920
And you could have said the
corresponding angle here is

00:03:27.920 --> 00:03:30.080
also here, so this
is 70 degrees.

00:03:30.080 --> 00:03:31.760
And then you could have said
all three of these are

00:03:31.760 --> 00:03:34.970
supplementary, and that they
would have to add up to 180.

00:03:34.970 --> 00:03:37.290
And you'd get z equals
30 either way.

00:03:37.290 --> 00:03:38.540
And that is choice A.

00:03:41.820 --> 00:03:43.070
Next problem.

00:03:47.570 --> 00:03:50.690
Problem 4.

00:03:50.690 --> 00:03:53.890
The scenic route from Mia's
home to her office is 5

00:03:53.890 --> 00:03:56.000
kilometers longer than
the direct route.

00:03:56.000 --> 00:03:57.600
So I'll call S for scenic.

00:03:57.600 --> 00:04:02.650
S is equal to the direct
route plus 4.

00:04:02.650 --> 00:04:05.375
The scenic route is 4 miles
longer than the direct route,

00:04:05.375 --> 00:04:07.030
or 4 kilometers.

00:04:07.030 --> 00:04:09.460
When she goes by the scenic
route and returns by the

00:04:09.460 --> 00:04:13.360
direct route, the round
trip is 35 kilometers.

00:04:13.360 --> 00:04:14.150
So that means what?

00:04:14.150 --> 00:04:18.010
The distance of the scenic route
plus the distance of the

00:04:18.010 --> 00:04:26.240
direct route is equal
to 35 kilometers.

00:04:26.240 --> 00:04:28.550
How many kilometers is
the direct route?

00:04:28.550 --> 00:04:31.010
So we want to solve for this.

00:04:31.010 --> 00:04:40.600
So this top equation, we can
rewrite this as S minus D is

00:04:40.600 --> 00:04:43.420
equal to 4.

00:04:43.420 --> 00:04:45.580
And actually just to make
things-- well, let me write

00:04:45.580 --> 00:04:46.270
that down right here.

00:04:46.270 --> 00:04:51.580
So you get S minus
D is equal to 4.

00:04:51.580 --> 00:04:54.240
And we can multiply this
equation by negative 1, so you

00:04:54.240 --> 00:04:56.840
cancel out the S's instead of
the D's, but since it's so

00:04:56.840 --> 00:04:58.560
convenient already, let's just
cancel out the D's and solve

00:04:58.560 --> 00:04:59.410
for the scenic route.

00:04:59.410 --> 00:05:00.610
The S's.

00:05:00.610 --> 00:05:03.080
So this is just a
system with two

00:05:03.080 --> 00:05:04.110
equations and two unknowns.

00:05:04.110 --> 00:05:06.180
So let's add these
two equations.

00:05:06.180 --> 00:05:11.740
So you get 2S-- D plus
D is 0-- is equal to

00:05:11.740 --> 00:05:18.430
35 plus 4 is 39.

00:05:18.430 --> 00:05:19.450
The numbers look strange.

00:05:19.450 --> 00:05:25.770
The scenic distance is 39/2.

00:05:25.770 --> 00:05:26.360
Right?

00:05:26.360 --> 00:05:28.390
That's 39/2 kilometers.

00:05:28.390 --> 00:05:29.640
And what is that equal to?

00:05:29.640 --> 00:05:31.190
If I were to write that
as a mixed number.

00:05:31.190 --> 00:05:31.840
Let's see.

00:05:31.840 --> 00:05:35.625
38 is-- that's 19 and
1/2 kilometers.

00:05:39.000 --> 00:05:40.620
A little less than
20 kilometers.

00:05:40.620 --> 00:05:42.060
That's the scenic route.

00:05:42.060 --> 00:05:44.950
The direct route is 4 less
than that, right?

00:05:44.950 --> 00:05:47.380
We said the scenic route is 4
more than the direct route.

00:05:47.380 --> 00:05:49.890
So the direct route is going
to be that minus 4.

00:05:49.890 --> 00:05:51.200
So what's 19 minus 4?

00:05:51.200 --> 00:05:53.760
It's 15, and then you still
have that half there.

00:05:53.760 --> 00:05:55.990
15 and 1/2 kilometers.

00:05:55.990 --> 00:05:58.370
And I don't see that
choice there, so I

00:05:58.370 --> 00:05:59.890
must have made a mistake.

00:05:59.890 --> 00:06:05.200
Let me do it here, just
to see where-- I

00:06:05.200 --> 00:06:06.270
don't see that choice.

00:06:06.270 --> 00:06:09.240
The scenic route from Mia's
home to her office is 5

00:06:09.240 --> 00:06:11.450
kilometers longer than
the direct route.

00:06:11.450 --> 00:06:12.350
Right.

00:06:12.350 --> 00:06:16.170
The scenic route-- we could even
say scenic route minus--

00:06:16.170 --> 00:06:18.100
oh, sorry, it's 5 kilometers
longer.

00:06:18.100 --> 00:06:19.020
Sorry.

00:06:19.020 --> 00:06:20.180
This is 5.

00:06:20.180 --> 00:06:21.730
That was my mistake.

00:06:21.730 --> 00:06:23.020
5 kilometers longer.

00:06:23.020 --> 00:06:25.470
Scenic minus direct is 5.

00:06:25.470 --> 00:06:27.120
They normally don't give weird
numbers like that.

00:06:27.120 --> 00:06:29.350
So this is 5.

00:06:29.350 --> 00:06:31.150
This is 40.

00:06:31.150 --> 00:06:33.360
This is 40/2.

00:06:33.360 --> 00:06:34.540
This is 20.

00:06:34.540 --> 00:06:35.940
Hope I'm not confusing you.

00:06:35.940 --> 00:06:38.280
And then if you're going to be
5 less than 20, it's going to

00:06:38.280 --> 00:06:40.220
be 15 kilometers, right?

00:06:40.220 --> 00:06:43.030
I hope you see what
I just did.

00:06:43.030 --> 00:06:45.140
I wrote 4 kilometers longer
instead of 5.

00:06:45.140 --> 00:06:48.250
That was my mistake, which
you should avoid.

00:06:48.250 --> 00:06:49.500
Next problem.

00:06:53.350 --> 00:06:54.120
Let me switch colors.

00:06:54.120 --> 00:06:58.880
I think that yellow induces
careless mistakes.

00:06:58.880 --> 00:06:59.950
5.

00:06:59.950 --> 00:07:03.650
A complete cycle of a traffic
light takes 80 seconds.

00:07:03.650 --> 00:07:10.030
During each cycle, the light
is green for 40 seconds.

00:07:10.030 --> 00:07:17.260
Amber-- I guess that's red--
amber for 10 seconds.

00:07:17.260 --> 00:07:18.380
Oh, I guess amber is yellow.

00:07:18.380 --> 00:07:19.400
I don't know my colors.

00:07:19.400 --> 00:07:22.690
And red for 30 seconds.

00:07:22.690 --> 00:07:25.020
And the whole cycle
takes 80 seconds.

00:07:25.020 --> 00:07:27.500
If you add those up.

00:07:27.500 --> 00:07:30.170
At a randomly chosen time, what
is the probability that

00:07:30.170 --> 00:07:32.630
the light will not be red?

00:07:32.630 --> 00:07:34.470
So the probability that the
light will not be red is the

00:07:34.470 --> 00:07:37.980
probability that it's going
to be green or amber.

00:07:37.980 --> 00:07:43.730
And it's green or amber for 40
plus 10, for 50 seconds out of

00:07:43.730 --> 00:07:45.570
a total of 80 seconds, right?

00:07:45.570 --> 00:07:48.290
So the probability that when
you randomly walk up to the

00:07:48.290 --> 00:07:51.260
light, that it's going to be
green or amber-- or not red--

00:07:51.260 --> 00:07:53.370
is going to be 50 seconds.

00:07:53.370 --> 00:07:57.180
50/80, which is 5/8.

00:07:57.180 --> 00:08:01.030
And that is choice B.

00:08:01.030 --> 00:08:02.280
Next problem.

00:08:04.520 --> 00:08:06.430
Problem 6.

00:08:06.430 --> 00:08:09.310
For a certain hot water heater,
the increase in

00:08:09.310 --> 00:08:12.640
heating expenses is directly
proportional to the increase

00:08:12.640 --> 00:08:14.680
in the water temperature
setting.

00:08:14.680 --> 00:08:19.960
If heating expenses increase
by $24 when the water

00:08:19.960 --> 00:08:23.460
temperature is increased by
20 degrees Fahrenheit-- so

00:08:23.460 --> 00:08:33.780
expense goes up by 24 when
temperature is increased by 20

00:08:33.780 --> 00:08:37.630
degrees Fahrenheit.

00:08:37.630 --> 00:08:40.159
By how much will heating
expenses increase when the

00:08:40.159 --> 00:08:43.030
water temperature setting is
increased by 15 degrees

00:08:43.030 --> 00:08:43.900
Fahrenheit?

00:08:43.900 --> 00:08:46.210
So this is just a
ratio problem.

00:08:46.210 --> 00:08:52.160
So you say, well, the expenses
go up $24 when we have a

00:08:52.160 --> 00:08:54.990
20-degree increase
in temperature.

00:08:54.990 --> 00:08:58.340
So then how many dollars will
it increase when you have a

00:08:58.340 --> 00:09:00.780
15-degree increase?

00:09:00.780 --> 00:09:04.280
The denominator in both cases
was the change in temperature.

00:09:04.280 --> 00:09:06.160
And then this is the
change in expense.

00:09:06.160 --> 00:09:08.410
The triangle means
change, right?

00:09:08.410 --> 00:09:10.920
So you just have to make sure
that the ratios are consistent

00:09:10.920 --> 00:09:11.830
and let's just multiply.

00:09:11.830 --> 00:09:15.990
You get 20-- actually, and so
we don't have to get big

00:09:15.990 --> 00:09:18.420
numbers, let me reduce
this fraction.

00:09:18.420 --> 00:09:19.350
Divide the top and the bottom.

00:09:19.350 --> 00:09:24.500
This is the same thing as
6/5 is equal to x/15.

00:09:24.500 --> 00:09:25.920
This is easier to
multiply now.

00:09:25.920 --> 00:09:30.820
You get 5x is equal
to 15 times 6.

00:09:30.820 --> 00:09:32.400
Divide both sides by 5.

00:09:32.400 --> 00:09:37.070
You get x is equal to 15
times 6 divided by 5.

00:09:37.070 --> 00:09:40.460
That's 3, that's 1, that's 18.

00:09:40.460 --> 00:09:45.240
So the change in expense will
be $18, and that's choice B.

00:09:45.240 --> 00:09:47.060
See you in the next video.


SAT Prep: Test 6 Section 9 Part 2

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:04.440
We are on problem 7.

00:00:04.440 --> 00:00:05.705
Let me draw what they
have drawn.

00:00:08.670 --> 00:00:11.810
They drew a right triangle.

00:00:11.810 --> 00:00:14.380
The right triangle looks
something like this.

00:00:17.840 --> 00:00:18.990
And then they drew
another triangle.

00:00:18.990 --> 00:00:21.150
And it looks like an isosceles
triangle, although we can't

00:00:21.150 --> 00:00:25.600
assume anything in this life.

00:00:28.290 --> 00:00:31.795
Nothing comes for free.

00:00:31.795 --> 00:00:34.950
So this is x.

00:00:34.950 --> 00:00:37.410
This is y.

00:00:37.410 --> 00:00:40.560
u, v, w.

00:00:40.560 --> 00:00:41.590
Those are the angles.

00:00:41.590 --> 00:00:44.790
In the triangles above, what
is the average-- arithmetic

00:00:44.790 --> 00:00:51.860
mean-- of u, v, w, x, and y?

00:00:51.860 --> 00:00:55.310
So you have to just add up the
sum of the angles and then

00:00:55.310 --> 00:00:56.420
divide by the number
of angles.

00:00:56.420 --> 00:01:03.020
So we want to take u plus v plus
w plus x plus y, and then

00:01:03.020 --> 00:01:04.239
divide by the number
of angles.

00:01:04.239 --> 00:01:08.030
So there's one, two, three,
four, five angles.

00:01:08.030 --> 00:01:09.630
First question.

00:01:09.630 --> 00:01:12.250
What is u plus v plus w?

00:01:14.750 --> 00:01:17.065
Well, they form the angles in
a triangle, so they're going

00:01:17.065 --> 00:01:19.740
to add up to 180 degrees.

00:01:19.740 --> 00:01:21.820
And what's x plus y?

00:01:21.820 --> 00:01:24.680
Well, it's a right triangle.

00:01:24.680 --> 00:01:27.875
And all three of these angles
have to add up to 180.

00:01:27.875 --> 00:01:33.080
x plus y plus this 90 have
to add up to 180.

00:01:33.080 --> 00:01:36.480
So x plus y is going
to be equal to 90.

00:01:36.480 --> 00:01:38.580
Just subtract 90 from
both sides.

00:01:38.580 --> 00:01:42.200
So x plus y is equal to 90.

00:01:42.200 --> 00:01:46.640
So if we take the sum of the
top, 180 plus 90, that's 270.

00:01:46.640 --> 00:01:48.650
Divided by 5.

00:01:48.650 --> 00:01:56.920
5 goes into 270-- 5,
25, 7, 20, 54.

00:01:56.920 --> 00:01:59.036
So the average is 54 degrees.

00:01:59.036 --> 00:02:03.180
That's the arithmetic mean
of all of those angles.

00:02:03.180 --> 00:02:04.430
And that is choice E.

00:02:06.980 --> 00:02:08.230
Next problem.

00:02:10.636 --> 00:02:14.050
I just inadvertently switched
back to my bad-luck yellow.

00:02:14.050 --> 00:02:14.920
All right.

00:02:14.920 --> 00:02:16.870
Problem 8.

00:02:16.870 --> 00:02:25.510
Looks like they've drawn--
It looks like a ray.

00:02:25.510 --> 00:02:28.642
I'm going to put an
arrow on one side.

00:02:28.642 --> 00:02:31.860
Let me switch colors.

00:02:31.860 --> 00:02:38.120
They say that this is
x to the third.

00:02:38.120 --> 00:02:42.940
This is x squared.

00:02:42.940 --> 00:02:46.040
This is x.

00:02:46.040 --> 00:02:48.970
If x, x squared, and x to the
third lie on a number line in

00:02:48.970 --> 00:02:51.090
the order shown above, which of
the following could be the

00:02:51.090 --> 00:02:52.680
value of x?

00:02:52.680 --> 00:02:57.910
So the first thing we know, x
has got to be-- well, the

00:02:57.910 --> 00:03:00.240
first thing we know, that
x is a positive number.

00:03:00.240 --> 00:03:01.940
How do I know that?

00:03:01.940 --> 00:03:06.330
Because if x was not a positive
number-- well, let me

00:03:06.330 --> 00:03:07.690
think about that.

00:03:07.690 --> 00:03:08.590
Right.

00:03:08.590 --> 00:03:10.810
x has to be a positive number.

00:03:10.810 --> 00:03:11.770
Because-- let me put
it this way.

00:03:11.770 --> 00:03:18.270
If any negative number-- let's
say it's negative 1/2.

00:03:18.270 --> 00:03:25.090
If you square negative 1/2,
you get positive 1/4.

00:03:25.090 --> 00:03:29.080
So for any negative number,
the square is going to be

00:03:29.080 --> 00:03:31.420
bigger than the number itself.

00:03:31.420 --> 00:03:34.550
So we know that x is
greater than 0.

00:03:34.550 --> 00:03:36.210
That's one thing we know.

00:03:36.210 --> 00:03:37.670
What else do we know?

00:03:37.670 --> 00:03:40.410
We also know that x is going
to be less than 1.

00:03:40.410 --> 00:03:42.000
How do I know that?

00:03:42.000 --> 00:03:44.640
Because x squared
is less than x.

00:03:44.640 --> 00:03:47.680
And that only applies for
numbers less than 1.

00:03:47.680 --> 00:03:50.870
Because 1/2 squared is
equal to 1/4, and 1/4

00:03:50.870 --> 00:03:52.280
is less than 1/2.

00:03:52.280 --> 00:03:53.990
So we also know that
x is less than 1.

00:03:53.990 --> 00:03:56.520
So we just have to find a choice
where x is greater than

00:03:56.520 --> 00:03:59.240
0 and less than 1.

00:03:59.240 --> 00:04:03.390
And if we look at the choices,
greater than 0 and less than

00:04:03.390 --> 00:04:06.510
1, there's only one choice
that that applies to.

00:04:06.510 --> 00:04:08.800
And that's 3/4.

00:04:08.800 --> 00:04:10.730
Choice C.

00:04:10.730 --> 00:04:12.420
You might want to say 3/2,
but that's 1 and 1/2.

00:04:12.420 --> 00:04:13.670
That's greater than 1.

00:04:13.670 --> 00:04:14.820
The first two choices
are negative.

00:04:14.820 --> 00:04:17.339
The last two choices are greater
than 1-- or greater

00:04:17.339 --> 00:04:18.640
than or equal to 1.

00:04:18.640 --> 00:04:20.660
So we know it's choice C.

00:04:20.660 --> 00:04:21.910
Next problem.

00:04:26.900 --> 00:04:29.080
And if you didn't want to do it
in an abstract way, and if

00:04:29.080 --> 00:04:30.640
you have a lot of time, if
you're really fast on the

00:04:30.640 --> 00:04:31.560
problems you do know
how to do, you can

00:04:31.560 --> 00:04:32.460
always try out the numbers.

00:04:32.460 --> 00:04:33.710
But that takes longer.

00:04:36.590 --> 00:04:39.210
They drew a coordinate
system right here.

00:04:42.950 --> 00:04:46.150
And this is my y-axis.

00:04:46.150 --> 00:04:48.910
This is the x-axis.

00:04:48.910 --> 00:04:52.100
And then they draw a line that
goes through the origin.

00:05:00.530 --> 00:05:06.420
And then they tell us that this
point right here is the

00:05:06.420 --> 00:05:08.215
point 1 comma 3.

00:05:08.215 --> 00:05:10.160
So this is 1.

00:05:10.160 --> 00:05:12.120
This is 3.

00:05:12.120 --> 00:05:13.560
And what do they want
us to do with this?

00:05:13.560 --> 00:05:16.420
In the figure above, line l
passes through the origin.

00:05:16.420 --> 00:05:18.600
This is line l.

00:05:18.600 --> 00:05:20.710
What is the value of k/h?

00:05:20.710 --> 00:05:23.820
Oh, and then they label
another point here.

00:05:23.820 --> 00:05:29.200
They say this is h comma k.

00:05:29.200 --> 00:05:33.090
So what is the value
of k divided by h?

00:05:33.090 --> 00:05:41.300
So the y value over the
x value, right?

00:05:41.300 --> 00:05:43.890
And I'm going to tell you right
now, the value of it is

00:05:43.890 --> 00:05:46.680
going to be the slope
of this line.

00:05:46.680 --> 00:05:47.930
And how do we know that?

00:05:50.580 --> 00:05:55.980
If you wanted to figure out the
slope from the origin to

00:05:55.980 --> 00:05:57.930
this point, what would it be?

00:05:57.930 --> 00:06:00.910
The origin of course is 0, 0.

00:06:00.910 --> 00:06:02.340
So it would be change in y.

00:06:02.340 --> 00:06:04.710
Change in y is 0 minus k.

00:06:04.710 --> 00:06:05.740
You wouldn't have to
do this on the SAT.

00:06:05.740 --> 00:06:07.840
I just want to show you that
it would be the slope.

00:06:07.840 --> 00:06:14.060
And then change in x
would be 0 minus h.

00:06:14.060 --> 00:06:17.060
And that of course is equal
to minus k over minus h.

00:06:17.060 --> 00:06:20.360
The negatives cancel out,
and that equals k/h.

00:06:20.360 --> 00:06:22.520
So they're essentially just
asking us, what is the slope

00:06:22.520 --> 00:06:23.630
of this line?

00:06:23.630 --> 00:06:24.770
Well, that's easy enough,
because it

00:06:24.770 --> 00:06:26.120
gives us another point.

00:06:26.120 --> 00:06:29.530
And so we can say, well, we
could do this rise over run.

00:06:29.530 --> 00:06:31.350
So here, what is the
change in y?

00:06:31.350 --> 00:06:34.410
Change in y is equal
to 3 minus 0.

00:06:34.410 --> 00:06:36.180
I'm taking this as kind
of the initial point.

00:06:36.180 --> 00:06:37.660
3 minus 0.

00:06:37.660 --> 00:06:40.560
Change in x is 1 minus 0.

00:06:40.560 --> 00:06:43.900
So change in y over change
in x is equal to 3.

00:06:43.900 --> 00:06:45.460
And that's our slope, and
that's our answer.

00:06:45.460 --> 00:06:48.760
So the answer is A.

00:06:48.760 --> 00:06:52.290
Next problem.

00:06:52.290 --> 00:06:57.820
Problem 10.

00:06:57.820 --> 00:07:00.410
They're saying the absolute
value of m minus

00:07:00.410 --> 00:07:03.130
3 is equal to 5.

00:07:03.130 --> 00:07:08.850
They're also telling us that the
absolute value of k plus 7

00:07:08.850 --> 00:07:10.655
is equal to 15.

00:07:10.655 --> 00:07:14.640
In the equations above,
m is less than 0 and k

00:07:14.640 --> 00:07:15.890
is less than 0.

00:07:20.190 --> 00:07:24.410
What is the value
of m minus k?

00:07:24.410 --> 00:07:27.230
So m is less than 0, right?

00:07:27.230 --> 00:07:30.450
So there's two possibilities
here.

00:07:30.450 --> 00:07:32.660
This first equation, if we
didn't see that, it could mean

00:07:32.660 --> 00:07:33.390
two different things.

00:07:33.390 --> 00:07:38.790
You could say m minus 3 is equal
to 5 or m minus 3 is

00:07:38.790 --> 00:07:41.050
equal to negative 5.

00:07:41.050 --> 00:07:44.050
This one would solve to m is
equal to 8, and this one would

00:07:44.050 --> 00:07:47.840
solve to m is equal
to minus 2.

00:07:47.840 --> 00:07:52.390
Well, we know m is not 8,
because m is less than 0.

00:07:52.390 --> 00:07:54.510
And to solve this, I just
added 3 to both sides.

00:07:54.510 --> 00:07:56.690
So we know that m is minus 2.

00:07:56.690 --> 00:07:59.610
Similarly, let's take that
second equation.

00:07:59.610 --> 00:08:07.220
That tells us that k plus 7 is
equal to 15, or k plus 7 is

00:08:07.220 --> 00:08:09.210
equal to minus 15.

00:08:09.210 --> 00:08:12.010
Subtract 7 from both sides of
this, you get k equals 8.

00:08:12.010 --> 00:08:14.270
Subtract 7 from both sides
of this, you get k is

00:08:14.270 --> 00:08:16.810
equal to minus 22.

00:08:16.810 --> 00:08:20.530
And they tell us that k
is also less than 0.

00:08:20.530 --> 00:08:22.980
So we know that this is k.

00:08:22.980 --> 00:08:27.980
And they want us to know
what m minus k is.

00:08:27.980 --> 00:08:32.390
Well, m is minus 2,
and k is minus 22.

00:08:32.390 --> 00:08:36.422
So minus 2 minus minus 22.

00:08:36.422 --> 00:08:40.090
So that's the same thing
as minus 2 plus 22.

00:08:40.090 --> 00:08:43.030
And that is of course 20.

00:08:43.030 --> 00:08:44.920
And that is choice E.

00:08:48.030 --> 00:08:50.620
I will see you in
the next video.


SAT Prep: Test 6 Section 9 Part 3

WEBVTT
Kind: captions
Language: en

00:00:00.900 --> 00:00:02.240
We are on problem number 11.

00:00:02.240 --> 00:00:04.040
I wrote out that chart,
although you

00:00:04.040 --> 00:00:05.145
probably can't read it.

00:00:05.145 --> 00:00:08.460
So they say, according to the
table above, car engine oil

00:00:08.460 --> 00:00:14.800
with a rating of 5w flows how
many times as fast as a car

00:00:14.800 --> 00:00:18.100
engine oil with a
rating of 20w?

00:00:18.100 --> 00:00:21.970
So how much faster
is 5w versus 20w?

00:00:21.970 --> 00:00:24.650
So let's read the chart.

00:00:24.650 --> 00:00:28.430
It says 10w is half
as fast as 5w.

00:00:28.430 --> 00:00:31.860
So 5w is twice as fast as 10w.

00:00:31.860 --> 00:00:37.340
So 5w is 2 times 10w.

00:00:37.340 --> 00:00:42.740
Then they tell us that 15w
is half as fast as 10w.

00:00:42.740 --> 00:00:46.190
So 10w is double the
speed of 15w.

00:00:46.190 --> 00:00:47.040
Actually, let's do
it that way.

00:00:47.040 --> 00:00:50.000
10w is double the speed
of 15w, right?

00:00:50.000 --> 00:00:53.980
And then 15w is double
the speed of 20w.

00:00:53.980 --> 00:00:55.250
So you have two doublings.

00:00:55.250 --> 00:00:58.710
So 10w is going to be 4 times as
fast. It's 2 times as fast

00:00:58.710 --> 00:01:01.040
as this, which is 2 times
as fast as this.

00:01:01.040 --> 00:01:05.230
So 10w is 4 times
faster than 20w.

00:01:05.230 --> 00:01:13.540
So 10w is 4 times 20w.

00:01:13.540 --> 00:01:16.180
And 5w is twice 10w.

00:01:16.180 --> 00:01:20.820
So 5w is going to
be 8 times 20w.

00:01:20.820 --> 00:01:23.460
And really, the most confusing
thing about this is the fact

00:01:23.460 --> 00:01:27.180
that these labels for these
ratings involve numbers that

00:01:27.180 --> 00:01:29.380
aren't proportional to actually
how much faster they

00:01:29.380 --> 00:01:30.130
are than each other.

00:01:30.130 --> 00:01:36.230
You could actually change this
to x, y, z, and then it might

00:01:36.230 --> 00:01:37.700
be a little bit easier.

00:01:37.700 --> 00:01:39.180
But that's all there is to it.

00:01:39.180 --> 00:01:40.830
This is twice as fast
as this, which is

00:01:40.830 --> 00:01:42.340
twice as fast as this.

00:01:42.340 --> 00:01:45.980
And if you were at 5w up here,
so 5w is twice as fast as

00:01:45.980 --> 00:01:47.940
this, which is twice as fast
as this, which is twice as

00:01:47.940 --> 00:01:48.610
fast as that.

00:01:48.610 --> 00:01:51.000
So you're doubling three times,
so it's 8 times as

00:01:51.000 --> 00:01:54.600
fast. And that's choice C.

00:01:54.600 --> 00:01:55.850
Next problem.

00:02:00.747 --> 00:02:02.050
Let me draw that.

00:02:05.487 --> 00:02:07.195
We have a line like that.

00:02:09.775 --> 00:02:11.025
Straight line at the bottom.

00:02:15.085 --> 00:02:17.420
Then we have a line.

00:02:17.420 --> 00:02:18.880
Looks something like that.

00:02:24.020 --> 00:02:34.350
And this is P, A, Q, B, R.

00:02:34.350 --> 00:02:35.860
This is line m.

00:02:35.860 --> 00:02:38.290
This is line l.

00:02:38.290 --> 00:02:39.610
Figure not drawn to the scale.

00:02:39.610 --> 00:02:40.590
Sure.

00:02:40.590 --> 00:02:44.790
In the figure above, points
P, A, and B are equally

00:02:44.790 --> 00:02:46.590
spaced on line l.

00:02:46.590 --> 00:02:48.110
Equally spaced.

00:02:48.110 --> 00:02:50.470
So that means that the distance
from P to A is equal

00:02:50.470 --> 00:02:51.660
to the distance from A to B.

00:02:51.660 --> 00:02:52.940
They're equally spaced.

00:02:52.940 --> 00:02:55.560
That's good to know.

00:02:55.560 --> 00:02:59.500
And points P, Q, and R are
equally spaced on line m.

00:02:59.500 --> 00:03:00.450
OK.

00:03:00.450 --> 00:03:02.030
So P, Q, and R are
equally spaced.

00:03:02.030 --> 00:03:03.580
It didn't look like it
the way I drew it.

00:03:03.580 --> 00:03:06.310
But so this is equal to this.

00:03:09.430 --> 00:03:17.630
If PB is equal to 4-- so that
entire thing is equal to 4.

00:03:17.630 --> 00:03:18.850
So we immediately know
that this is 2

00:03:18.850 --> 00:03:20.110
and this is 2, right?

00:03:20.110 --> 00:03:23.110
Because they're equally
spaced.

00:03:23.110 --> 00:03:24.940
PR is equal to 6.

00:03:24.940 --> 00:03:29.020
So this entire thing
is equal to 6.

00:03:29.020 --> 00:03:33.410
So we know that this
is 3 and this is 3.

00:03:33.410 --> 00:03:35.445
And AQ is 4.

00:03:41.760 --> 00:03:44.760
What is the perimeter of
quadrilateral QABR?

00:03:47.510 --> 00:03:49.015
Let's see, where is Q?

00:03:49.015 --> 00:03:50.265
QABR.

00:03:52.110 --> 00:03:53.660
So we know this side.

00:03:53.660 --> 00:03:55.700
We know this side.

00:03:55.700 --> 00:03:56.880
We know this side.

00:03:56.880 --> 00:04:00.290
We just have to figure
out this side.

00:04:03.615 --> 00:04:06.970
And I'll tell you right now
that this is going to be a

00:04:06.970 --> 00:04:09.145
similar triangle problem,
I believe.

00:04:11.940 --> 00:04:14.530
Because these triangles are
going to be proportional to

00:04:14.530 --> 00:04:15.340
each other.

00:04:15.340 --> 00:04:16.590
How do I know that?

00:04:21.769 --> 00:04:23.260
I'm going to draw two
triangles for you.

00:04:23.260 --> 00:04:31.120
You have this big triangle,
and then you have

00:04:31.120 --> 00:04:32.370
this smaller triangle.

00:04:37.150 --> 00:04:38.790
And the big triangle is similar

00:04:38.790 --> 00:04:40.030
to the smaller triangle.

00:04:40.030 --> 00:04:40.980
And how do I know that?

00:04:40.980 --> 00:04:42.960
Well, they share
an angle here.

00:04:42.960 --> 00:04:48.730
and we know that the bigger
triangle, two of its sides are

00:04:48.730 --> 00:04:52.620
just double the sides of
the other two angles.

00:04:52.620 --> 00:04:53.600
Or-- I'm sorry.

00:04:53.600 --> 00:04:58.080
We know that, for example, this
side on the big triangle

00:04:58.080 --> 00:05:02.610
is double this side on the
small triangle, right?

00:05:02.610 --> 00:05:02.950
Similar.

00:05:02.950 --> 00:05:06.725
We know this big side on the
big triangle is double this

00:05:06.725 --> 00:05:08.980
side on the small triangle.

00:05:08.980 --> 00:05:11.760
So two sides are proportional
to each other.

00:05:11.760 --> 00:05:12.620
We have one common angle.

00:05:12.620 --> 00:05:15.550
We know that this is
a similar triangle.

00:05:15.550 --> 00:05:18.840
So we know that this side is
going to be double this side.

00:05:18.840 --> 00:05:21.390
So this side is going to be 8.

00:05:21.390 --> 00:05:22.980
And you could have probably
guessed that even if you

00:05:22.980 --> 00:05:24.530
didn't want to prove that
they're similar triangles.

00:05:24.530 --> 00:05:25.640
So this is 8.

00:05:25.640 --> 00:05:27.840
The perimeter that we had to
figure out to begin with--

00:05:27.840 --> 00:05:31.440
this is the quadrilateral
right here.

00:05:31.440 --> 00:05:38.230
It's going to be 8 plus
3 plus 4 plus 2.

00:05:38.230 --> 00:05:39.280
And what is that?

00:05:39.280 --> 00:05:41.140
That's 8 plus-- 17.

00:05:41.140 --> 00:05:41.460
Right?

00:05:41.460 --> 00:05:42.860
6, 9, right.

00:05:42.860 --> 00:05:43.580
17.

00:05:43.580 --> 00:05:45.770
And that is choice E.

00:05:45.770 --> 00:05:47.020
Next problem.

00:05:52.880 --> 00:05:55.330
Problem 13.

00:05:55.330 --> 00:05:55.580
OK.

00:05:55.580 --> 00:05:57.810
13 and 14 refer to
these functions.

00:05:57.810 --> 00:06:04.260
So g of n is equal to
n squared plus n.

00:06:04.260 --> 00:06:10.060
h of n is equal to n
squared minus n.

00:06:10.060 --> 00:06:10.760
So the first problem.

00:06:10.760 --> 00:06:15.920
They want to know what g
of 5 minus h of 4 is.

00:06:15.920 --> 00:06:16.910
So g of 5.

00:06:16.910 --> 00:06:19.700
Let's stick in 5 into g.

00:06:19.700 --> 00:06:23.280
So you get 5 squared plus 5.

00:06:23.280 --> 00:06:25.220
I just replace 5 where n is.

00:06:25.220 --> 00:06:27.960
And then we're going
to subtract h of n.

00:06:27.960 --> 00:06:30.030
So what's h of n?

00:06:30.030 --> 00:06:31.175
Oh, sorry, h of 4.

00:06:31.175 --> 00:06:32.570
It looked like an n.

00:06:32.570 --> 00:06:34.160
And h of 4.

00:06:34.160 --> 00:06:38.675
So h of 4 is 4 squared
minus 4.

00:06:38.675 --> 00:06:39.710
And so let's simplify this.

00:06:39.710 --> 00:06:46.750
That's 25 plus 5 minus
16 plus 4.

00:06:46.750 --> 00:06:47.370
So that's what?

00:06:47.370 --> 00:06:53.620
30 minus 16 plus 4.

00:06:53.620 --> 00:07:00.710
30 minus 16 is 14, plus
4, so it's 18.

00:07:00.710 --> 00:07:03.680
So that is choice D.

00:07:03.680 --> 00:07:04.000
All right.

00:07:04.000 --> 00:07:06.115
Problem 14 also applies
to this.

00:07:06.115 --> 00:07:07.470
So I'll do it right here.

00:07:07.470 --> 00:07:11.855
Which of the following is
equivalent to h of m plus 1?

00:07:16.210 --> 00:07:18.430
So we essentially just,
everywhere we see an n here,

00:07:18.430 --> 00:07:20.170
we put an m plus 1.

00:07:20.170 --> 00:07:23.715
So h of m plus 1 is equal to--
we see an n, so we put an m

00:07:23.715 --> 00:07:24.890
plus 1 there.

00:07:24.890 --> 00:07:31.890
m plus 1 squared minus-- instead
of an n-- m plus 1.

00:07:31.890 --> 00:07:32.780
Multiply that out.

00:07:32.780 --> 00:07:41.510
You get m squared plus 2m plus
1, and then minus m minus 1.

00:07:41.510 --> 00:07:42.190
Let's see.

00:07:42.190 --> 00:07:45.870
So this 1 and this
1 cancel out.

00:07:45.870 --> 00:07:47.680
And then 2m minus m.

00:07:47.680 --> 00:07:52.410
So you're left with
m squared minus m.

00:07:54.920 --> 00:08:00.730
So h of m plus 1 is equal
to m squared minus m.

00:08:00.730 --> 00:08:05.050
But isn't that the same
thing as h of m?

00:08:05.050 --> 00:08:07.140
Reminds me of that store.

00:08:07.140 --> 00:08:09.970
That's H&M, not h of m, although
that would be a fun

00:08:09.970 --> 00:08:11.530
name for a store as well.

00:08:11.530 --> 00:08:12.600
h of m.

00:08:12.600 --> 00:08:13.380
Well, what's h of m?

00:08:13.380 --> 00:08:14.590
You put an m where
you see an n.

00:08:14.590 --> 00:08:17.300
So that also equals
m squared minus m.

00:08:17.300 --> 00:08:18.720
So the answer is h of m.

00:08:18.720 --> 00:08:20.970
And let me now look
at the choices.

00:08:20.970 --> 00:08:23.060
And that is not there.

00:08:23.060 --> 00:08:24.920
So I have made a mistake.

00:08:27.610 --> 00:08:31.790
m squared plus 1.

00:08:31.790 --> 00:08:34.710
They're saying, which of the
following is equal to h of m--

00:08:34.710 --> 00:08:38.700
let me clear things.

00:08:38.700 --> 00:08:39.760
OK.

00:08:39.760 --> 00:08:42.120
So they say, which of the
following is equivalent to h

00:08:42.120 --> 00:08:43.799
of m plus 1?

00:08:47.475 --> 00:08:51.130
And that is equal to
h of m, right?

00:08:51.130 --> 00:08:51.440
Right.

00:08:51.440 --> 00:09:02.440
That is equal to m plus 1
squared minus m plus 1.

00:09:02.440 --> 00:09:09.420
That's m squared plus 2m plus
1, minus m, minus 1.

00:09:09.420 --> 00:09:13.520
So that's m squared-- plus m.

00:09:13.520 --> 00:09:14.200
Oh, sorry.

00:09:14.200 --> 00:09:15.250
Plus m.

00:09:15.250 --> 00:09:16.200
m squared plus m.

00:09:16.200 --> 00:09:18.440
And then this cancels out.

00:09:18.440 --> 00:09:24.190
So h of m plus 1 is equal
to m squared plus m.

00:09:24.190 --> 00:09:24.570
Right?

00:09:24.570 --> 00:09:26.220
And what's m squared plus m?

00:09:26.220 --> 00:09:29.910
Well, that's the same
thing as g of m.

00:09:29.910 --> 00:09:33.880
Because take g of n, or take
g of m and that's also m

00:09:33.880 --> 00:09:35.810
squared plus m.

00:09:35.810 --> 00:09:39.370
So that is choice A.

00:09:39.370 --> 00:09:41.940
Before I cleared it, my mistake
was when I did 2m

00:09:41.940 --> 00:09:45.040
minus m, I got, for some silly
reason, minus m instead of

00:09:45.040 --> 00:09:45.650
positive m.

00:09:45.650 --> 00:09:46.480
Should be a positive m.

00:09:46.480 --> 00:09:47.940
That was my mistake.

00:09:47.940 --> 00:09:49.190
I'll see you in the next video.


SAT Prep: Test 6 Section 9 Part 4

WEBVTT
Kind: captions
Language: en

00:00:00.780 --> 00:00:04.890
We are on problem 15.

00:00:04.890 --> 00:00:07.795
A store charges $28 for
a type of sweater.

00:00:10.880 --> 00:00:15.800
This price is 40% more than it
costs the store to buy one of

00:00:15.800 --> 00:00:16.980
these sweaters.

00:00:16.980 --> 00:00:22.370
So $28 is 40% more than
what it costs.

00:00:22.370 --> 00:00:29.750
So that equals the cost plus
40% of the cost. Right?

00:00:29.750 --> 00:00:32.090
0.4 is the same thing
as 40%, right?

00:00:32.090 --> 00:00:34.390
It's the cost plus 40%
of cost. That's

00:00:34.390 --> 00:00:35.890
what 40% more means.

00:00:35.890 --> 00:00:38.300
Another way, you could kind of
immediately say, well, that's

00:00:38.300 --> 00:00:41.840
just the same thing as 1.4 times
the cost. And that's

00:00:41.840 --> 00:00:43.560
kind of shorthand.

00:00:43.560 --> 00:00:46.410
You might immediately go to the
step, 1.4 times the cost

00:00:46.410 --> 00:00:47.800
OK, let's see what it says.

00:00:47.800 --> 00:00:51.110
At the end-of-season sale, store
employees can purchase

00:00:51.110 --> 00:00:56.900
any remaining sweaters at 30%
off the store's cost. So the

00:00:56.900 --> 00:01:01.600
sale price-- let me call that
s-- is equal to the cost minus

00:01:01.600 --> 00:01:03.910
0.3 times the cost. Right?

00:01:03.910 --> 00:01:07.820
30% off of the cost. This is 30%
of the cost. You take that

00:01:07.820 --> 00:01:10.390
off of the original cost. And
that is equal to, of course,

00:01:10.390 --> 00:01:13.885
0.7 times the cost. This
is the sale price.

00:01:13.885 --> 00:01:18.210
It's 0.7 times the cost. How
much would it cost an employee

00:01:18.210 --> 00:01:23.680
to purchase a sweater of
this type at this sale?

00:01:23.680 --> 00:01:24.720
So let's see.

00:01:24.720 --> 00:01:26.020
So how much would it cost?

00:01:26.020 --> 00:01:27.490
So we could figure
out what the cost

00:01:27.490 --> 00:01:29.070
is from this equation.

00:01:29.070 --> 00:01:35.900
We have 28 is equal to 1.4 times
the cost. Cost is equal

00:01:35.900 --> 00:01:38.670
to 28 divided by 1.4.

00:01:38.670 --> 00:01:40.280
I just divide both
sides by 1.4.

00:01:40.280 --> 00:01:42.240
I switched them around.

00:01:42.240 --> 00:01:46.190
Let's see, 28 divided by
14 would be 2, right?

00:01:46.190 --> 00:01:50.000
28 divided by 1.4 is 20.

00:01:50.000 --> 00:01:50.900
So that makes sense.

00:01:50.900 --> 00:01:52.170
And you could go
the other way.

00:01:52.170 --> 00:01:53.520
40% more than 20.

00:01:53.520 --> 00:01:55.110
40% of 20 is 8.

00:01:55.110 --> 00:01:56.540
You add 8 to 20, you get 28.

00:01:56.540 --> 00:01:57.160
So that's right.

00:01:57.160 --> 00:01:58.930
The cost is $20.

00:01:58.930 --> 00:02:03.000
And now the sale is 0.7 times
the cost. So sale is equal to

00:02:03.000 --> 00:02:06.450
0.7 times the cost. And
that equals what?

00:02:06.450 --> 00:02:12.060
20 times 0.7 is $14.

00:02:12.060 --> 00:02:13.690
Because 20 times 7 is 140.

00:02:13.690 --> 00:02:15.710
You have one decimal
place, $14.

00:02:15.710 --> 00:02:19.430
So that is choice B.

00:02:19.430 --> 00:02:21.220
Next problem.

00:02:21.220 --> 00:02:22.246
Problem 16.

00:02:22.246 --> 00:02:23.780
And then we're done
with this section.

00:02:27.310 --> 00:02:30.810
In rectangle ABCD-- let me
draw rectangle ABCD, even

00:02:30.810 --> 00:02:33.110
though they haven't.

00:02:33.110 --> 00:02:41.350
OK, rectangle-- whoops--
A, B, C, D.

00:02:41.350 --> 00:02:45.640
In rectangle ABCD, E is
the midpoint of BC.

00:02:45.640 --> 00:02:46.960
So let me draw E.

00:02:51.230 --> 00:02:54.930
So this distance is equal
to that distance.

00:02:54.930 --> 00:03:04.725
If the area of quadrilateral
ABED is 2/3, what is the area

00:03:04.725 --> 00:03:06.060
of the entire rectangle?

00:03:06.060 --> 00:03:06.620
Fascinating.

00:03:06.620 --> 00:03:10.505
So they're making another
quadrilateral within this.

00:03:10.505 --> 00:03:12.260
And I'll just draw it.

00:03:12.260 --> 00:03:13.880
Let me do it in another color.

00:03:13.880 --> 00:03:16.520
So they're saying the area
of this thing, ABED.

00:03:27.670 --> 00:03:31.470
Area of that thing is 2/3.

00:03:31.470 --> 00:03:32.790
And so they want you to
figure out the area

00:03:32.790 --> 00:03:33.540
of the whole thing.

00:03:33.540 --> 00:03:35.750
And so this is just a pure
visualization problem.

00:03:35.750 --> 00:03:39.410
Because what I can do is I can
break up this rectangle in a

00:03:39.410 --> 00:03:40.710
interesting way.

00:03:40.710 --> 00:03:43.480
Let me do it with this
brown color.

00:03:43.480 --> 00:03:50.920
If I wanted to break up this
rectangle, I could break it up

00:03:50.920 --> 00:03:52.780
into four equal triangles,
right?

00:03:57.100 --> 00:03:58.810
You see here, 1, 2, 3, 4.

00:03:58.810 --> 00:04:00.020
And how do I know
they're equal?

00:04:00.020 --> 00:04:01.570
Because E is the midpoint.

00:04:01.570 --> 00:04:05.730
We know that this side is equal
to this side, because E

00:04:05.730 --> 00:04:07.210
is the midpoint.

00:04:07.210 --> 00:04:13.680
We know that this is equal to
this, which is equal to this.

00:04:13.680 --> 00:04:16.339
So we know that all four of
these rectangles are going to

00:04:16.339 --> 00:04:17.450
be the same.

00:04:17.450 --> 00:04:20.120
Now, they tell us that the
area of three-- of this

00:04:20.120 --> 00:04:22.060
rectangle, this rectangle, and
this rectangle-- right?

00:04:22.060 --> 00:04:23.680
That's ABED.

00:04:23.680 --> 00:04:26.920
They tell us three of the
rectangles-- sorry, three of

00:04:26.920 --> 00:04:28.250
the triangles.

00:04:28.250 --> 00:04:29.550
Have I been saying rectangles
the whole time?

00:04:29.550 --> 00:04:30.350
These are triangles.

00:04:30.350 --> 00:04:32.550
ABEA, these are triangles.

00:04:32.550 --> 00:04:38.180
So this rectangle is made up
of four equal triangles.

00:04:38.180 --> 00:04:43.910
We know that three of the
triangles-- this quadrilateral

00:04:43.910 --> 00:04:46.290
here-- three of the
triangles, so I'll

00:04:46.290 --> 00:04:47.490
call them three triangles.

00:04:47.490 --> 00:04:51.590
So I'll call it 3 times
the area of each

00:04:51.590 --> 00:04:53.402
triangle is equal to what?

00:04:53.402 --> 00:04:56.290
It is equal to 2/3.

00:04:56.290 --> 00:04:58.640
And we know that because they
told us that the area of this

00:04:58.640 --> 00:05:00.040
plus this, plus this is 2/3.

00:05:00.040 --> 00:05:02.970
This quadrilateral is 2/3.

00:05:02.970 --> 00:05:04.810
So what's the area
of each triangle?

00:05:04.810 --> 00:05:09.160
The area of each triangle is
going to be 2/3 divided by 3,

00:05:09.160 --> 00:05:10.840
which is 2/9, right?

00:05:10.840 --> 00:05:12.900
2/3 times 1/3.

00:05:12.900 --> 00:05:15.430
Area of each triangle is 2/9.

00:05:15.430 --> 00:05:20.230
So what's going to be the area
of this entire rectangle?

00:05:20.230 --> 00:05:23.080
Well, it's going to be this
area-- that we just know is

00:05:23.080 --> 00:05:27.980
2/3-- plus the area of one
more triangle right here.

00:05:27.980 --> 00:05:29.240
Plus the area of
this triangle.

00:05:29.240 --> 00:05:31.170
And then we get the
whole rectangle.

00:05:31.170 --> 00:05:33.230
So plus 2/9.

00:05:33.230 --> 00:05:37.280
And this equals-- let's see,
common denominator is 9.

00:05:37.280 --> 00:05:39.290
2/3 becomes 6/9.

00:05:39.290 --> 00:05:44.720
And then you have that plus the
2/9, and this becomes 8/9.

00:05:44.720 --> 00:05:48.290
And that is choice C.

00:05:48.290 --> 00:05:49.100
And we are done.

00:05:49.100 --> 00:05:51.220
So this was a pure visualization
problem.

00:05:51.220 --> 00:05:53.930
You just had to see that the
area they gave you was three

00:05:53.930 --> 00:05:56.270
equal triangles, and they
essentially just want you to

00:05:56.270 --> 00:05:57.750
add the fourth onto it
and figure out what

00:05:57.750 --> 00:05:59.160
the total area is.

00:05:59.160 --> 00:06:01.110
I'll see you in the
next section.


SAT Prep: Test 6 Section 7 Part 3

WEBVTT
Kind: captions
Language: en

00:00:00.930 --> 00:00:01.520
Welcome back.

00:00:01.520 --> 00:00:03.610
I tried to start doing problem
number 10 in the last video,

00:00:03.610 --> 00:00:04.800
but I realized I was running
out of time, so

00:00:04.800 --> 00:00:06.240
let me start over.

00:00:06.240 --> 00:00:07.520
Problem number 10.

00:00:07.520 --> 00:00:10.180
The Smith Metals Company
old machine makes

00:00:10.180 --> 00:00:15.191
300 bolts per hour.

00:00:15.191 --> 00:00:23.410
Its new machine makes
450 bolts per hour.

00:00:23.410 --> 00:00:28.080
If both machines begin running
at the same time, how many

00:00:28.080 --> 00:00:31.420
minutes will it take the
two machines to make a

00:00:31.420 --> 00:00:33.330
total of 900 bolts?

00:00:33.330 --> 00:00:34.560
So the important thing
to realize is

00:00:34.560 --> 00:00:36.630
that they said minutes.

00:00:36.630 --> 00:00:39.580
So we could convert both of
these rates to minutes now, or

00:00:39.580 --> 00:00:42.120
we could say how many hours is
it going to take, and then

00:00:42.120 --> 00:00:47.180
convert that to minutes after
we have our answer.

00:00:47.180 --> 00:00:49.220
Actually, let's do it the second
way, let's say how many

00:00:49.220 --> 00:00:51.510
hours and then convert
that to minutes.

00:00:51.510 --> 00:00:58.560
So let's say we want to
produce 900 bolts.

00:00:58.560 --> 00:01:00.280
And how much are we going
to produce in each hour?

00:01:00.280 --> 00:01:02.800
Well, they're both running
at the same time, right?

00:01:02.800 --> 00:01:08.810
So in every hour, we're going to
produce 300 plus 450 bolts.

00:01:08.810 --> 00:01:18.260
We're going to produce
750 bolts per hour.

00:01:18.260 --> 00:01:21.500
Times, let's say x hours.

00:01:21.500 --> 00:01:24.530
The units might confuse you, so
just leave out the units.

00:01:24.530 --> 00:01:28.740
This is how many hours it takes
to produce 900 bolts, so

00:01:28.740 --> 00:01:31.460
you divide both sides by 750.

00:01:31.460 --> 00:01:36.620
You get x is equal to 900/750.

00:01:36.620 --> 00:01:38.350
Let's see what I can do here.

00:01:38.350 --> 00:01:44.040
See, if I divide the top and the
bottom by 30, the top will

00:01:44.040 --> 00:01:53.390
become 30 over-- and then the
bottom, 75 divided by 3 is

00:01:53.390 --> 00:01:57.540
20-- 75 divided by 3 is 25.

00:01:57.540 --> 00:02:00.280
So 30/25.

00:02:00.280 --> 00:02:02.890
Then I could-- let's see,
5 is a common factor.

00:02:02.890 --> 00:02:04.550
I can do it all in
one fell swoop.

00:02:04.550 --> 00:02:06.590
So that's 6/5.

00:02:06.590 --> 00:02:10.520
So it's going to
take 6/5 hours.

00:02:10.520 --> 00:02:11.680
That's how long it's
going to take us.

00:02:11.680 --> 00:02:13.470
How many minutes is that?

00:02:13.470 --> 00:02:15.910
Every hour is 1 minute--
I mean, sorry,

00:02:15.910 --> 00:02:17.420
every hour is 60 minutes.

00:02:17.420 --> 00:02:18.560
It's getting late.

00:02:18.560 --> 00:02:20.700
So 6/5 hours.

00:02:20.700 --> 00:02:23.660
You just have to multiply it by
60 to get how many minutes

00:02:23.660 --> 00:02:29.070
is equal to-- see, you can
cancel this 5, make this a 12.

00:02:29.070 --> 00:02:34.670
You get 6 times 12
is 72 minutes.

00:02:34.670 --> 00:02:37.730
And that is choice B.

00:02:37.730 --> 00:02:38.980
Next problem.

00:02:41.920 --> 00:02:45.050
I've been using this yellow
a while, let me switch.

00:02:45.050 --> 00:02:47.110
Problem 11.

00:02:47.110 --> 00:02:49.390
The table above gives the values
of the linear function

00:02:49.390 --> 00:02:51.620
g for selected values of t.

00:02:51.620 --> 00:02:54.130
Which of the following
defines g?

00:02:54.130 --> 00:03:01.570
OK, so they say t and
they say g of t.

00:03:01.570 --> 00:03:08.280
They go from negative 1, 0,
1, 2, let's see, it's

00:03:08.280 --> 00:03:16.450
4, 2, 0, minus 2.

00:03:16.450 --> 00:03:19.090
So the one thing I always look
at is what g of 0 is because

00:03:19.090 --> 00:03:20.080
that tends to be interesting.

00:03:20.080 --> 00:03:21.700
Especially when I look at
all of the choices.

00:03:21.700 --> 00:03:24.270
All of the choices are of this
form, they're all of the form

00:03:24.270 --> 00:03:26.220
m times t plus B.

00:03:26.220 --> 00:03:28.290
Where m is the slope-- if you're
familiar with linear

00:03:28.290 --> 00:03:30.060
equations, you're familiar
with this form.

00:03:30.060 --> 00:03:34.290
And so when t equals 0, g of t
tells you what the y-intercept

00:03:34.290 --> 00:03:36.040
is going to be, right?

00:03:36.040 --> 00:03:43.130
So let's see, g of
0 is equal to 2.

00:03:43.130 --> 00:03:46.710
So that tells us that this
equation g of t is going to be

00:03:46.710 --> 00:03:51.620
equal to the slope times
t plus 2, right?

00:03:51.620 --> 00:03:56.170
Because when t was 0, all
we had left with was 2.

00:03:56.170 --> 00:03:59.190
And so immediately, we can
cancel out all but the last

00:03:59.190 --> 00:04:00.915
two choices.

00:04:00.915 --> 00:04:05.470
So the last two choices, choice
D is g of t is equal to

00:04:05.470 --> 00:04:07.460
minus t plus 2.

00:04:07.460 --> 00:04:10.910
And then the last choice
is g of t is equal to

00:04:10.910 --> 00:04:13.650
minus 2t plus 2.

00:04:13.650 --> 00:04:15.050
Let's see which one of
these works, we can

00:04:15.050 --> 00:04:16.670
try out some numbers.

00:04:16.670 --> 00:04:19.450
So what happens when
t is negative 1?

00:04:19.450 --> 00:04:24.760
When t is negative 1, this
expression becomes negative 1

00:04:24.760 --> 00:04:25.950
times negative.

00:04:25.950 --> 00:04:29.550
Negative negative 1 is positive
1, so this becomes 3.

00:04:29.550 --> 00:04:31.080
That's not right.

00:04:31.080 --> 00:04:33.740
This one becomes negative
2 times negative 1 is

00:04:33.740 --> 00:04:36.630
positive 2, plus 2.

00:04:36.630 --> 00:04:39.600
So this becomes 4.

00:04:39.600 --> 00:04:41.830
So we can immediately cancel
this one out because it

00:04:41.830 --> 00:04:45.930
didn't-- here, for this g of t,
g of negative 1 equaled 3,

00:04:45.930 --> 00:04:47.980
and they tell us right here
it's supposed to equal 4.

00:04:47.980 --> 00:04:48.760
This one worked.

00:04:48.760 --> 00:04:50.300
And this is kind of the only
one that still works.

00:04:50.300 --> 00:04:52.750
It had a 2 for the y-intercept,
and when you

00:04:52.750 --> 00:04:54.660
evaluate it for just even
the first point, you

00:04:54.660 --> 00:04:55.650
got the right answer.

00:04:55.650 --> 00:04:57.230
So that's the answer,
the answer is E.

00:04:59.760 --> 00:05:01.010
Next problem.

00:05:06.650 --> 00:05:08.540
OK, survey results.

00:05:08.540 --> 00:05:10.150
I guess I should draw this.

00:05:10.150 --> 00:05:14.220
I haven't read the question, but
it's probably important.

00:05:14.220 --> 00:05:16.440
Let's see, there's about
five squares that way.

00:05:19.630 --> 00:05:33.950
So that means I have to draw
four lines, that's 1, 2, 3, 4.

00:05:33.950 --> 00:05:36.720
And then eight lines
I have to draw.

00:05:36.720 --> 00:05:39.790
1-- that's always the hardest
part, just drawing these

00:05:39.790 --> 00:05:49.320
diagrams-- 2, 3, 4-- and you're
learning how to count--

00:05:49.320 --> 00:05:59.230
5, 6, 7-- almost
there-- and 8.

00:05:59.230 --> 00:06:00.500
All righty.

00:06:00.500 --> 00:06:02.560
And then they say, these
are the grades--

00:06:02.560 --> 00:06:04.440
the y-axis is grade.

00:06:04.440 --> 00:06:08.990
Grade 9, 10, 11, 12.

00:06:08.990 --> 00:06:12.060
The x-axis is distance
to school in miles.

00:06:12.060 --> 00:06:16.450
1, 2, 3, 4, 5, 6, 7, 8.

00:06:16.450 --> 00:06:17.390
And these are the points.

00:06:17.390 --> 00:06:20.220
1 comma 10 is right here.

00:06:20.220 --> 00:06:23.330
2 comma 9.

00:06:23.330 --> 00:06:25.770
2 comma 11.

00:06:25.770 --> 00:06:29.260
3 comma 10.

00:06:29.260 --> 00:06:32.380
3 comma 12.

00:06:32.380 --> 00:06:36.440
4 comma-- let's see,
4 is at 10 and 11.

00:06:36.440 --> 00:06:40.290
5-- they have one point at 11.

00:06:40.290 --> 00:06:45.640
6 has three points right
here, 10, 11, and 12.

00:06:45.640 --> 00:06:47.080
Let's see.

00:06:47.080 --> 00:06:50.770
There's a point here,
here, here.

00:06:50.770 --> 00:06:52.470
And then a point
here and here.

00:06:52.470 --> 00:06:54.710
Now we can start the problem.

00:06:54.710 --> 00:06:57.490
The results of a survey of 16
students at Thompson High

00:06:57.490 --> 00:06:59.680
School are given in
the grid above.

00:06:59.680 --> 00:07:03.300
It shows the distance to the
nearest mile that students at

00:07:03.300 --> 00:07:05.180
various grade levels
travel to school.

00:07:05.180 --> 00:07:07.510
So this is miles.

00:07:07.510 --> 00:07:08.760
And this is grade.

00:07:10.740 --> 00:07:13.430
According to the grid, which
of the following is true?

00:07:13.430 --> 00:07:15.010
So I'll just read them out.

00:07:15.010 --> 00:07:17.180
A, there's only one student
who travels

00:07:17.180 --> 00:07:18.605
two miles to school.

00:07:18.605 --> 00:07:20.060
Let's see, two miles.

00:07:20.060 --> 00:07:22.050
False, there's two students.

00:07:22.050 --> 00:07:24.500
There is this guy
and this guy.

00:07:24.500 --> 00:07:25.600
So it's not A.

00:07:25.600 --> 00:07:28.540
Choice B, half of the students
travel less than

00:07:28.540 --> 00:07:31.500
four miles to school.

00:07:31.500 --> 00:07:34.250
So that's-- less than four miles
is everyone to the left

00:07:34.250 --> 00:07:35.450
of this line, right?

00:07:35.450 --> 00:07:38.490
And this is actually
1, 2, 3, 4, 5.

00:07:38.490 --> 00:07:43.800
5 out of 16 is not half, so
we know it's not choice B.

00:07:43.800 --> 00:07:47.640
C, more 12th graders than 11th
graders travel six miles or

00:07:47.640 --> 00:07:49.890
more to school.

00:07:49.890 --> 00:07:54.560
So they're saying more 12th
graders than 11th graders.

00:07:54.560 --> 00:07:57.110
So six miles or more.

00:07:57.110 --> 00:08:00.530
So let's see, six miles or more
is anything to the right

00:08:00.530 --> 00:08:01.310
of this line, right?

00:08:01.310 --> 00:08:03.090
That's six miles or more.

00:08:03.090 --> 00:08:05.670
There are three 12th graders.

00:08:05.670 --> 00:08:07.220
And how many 11th graders
are there?

00:08:09.850 --> 00:08:13.140
There are two 11th graders.

00:08:13.140 --> 00:08:14.770
I think that is correct.

00:08:14.770 --> 00:08:18.280
More 12th graders than 11th
graders travel six or more

00:08:18.280 --> 00:08:19.540
miles to school.

00:08:19.540 --> 00:08:24.430
Six or more miles, three 12th
graders, two 11th graders.

00:08:24.430 --> 00:08:28.420
That's our answer,
our answer is C.

00:08:28.420 --> 00:08:31.000
Next problem.

00:08:31.000 --> 00:08:34.950
I don't know if I'll have time
for this one, I'll try.

00:08:34.950 --> 00:08:37.520
Problem 13.

00:08:37.520 --> 00:08:42.429
How many positive three digit
integers have the hundreds

00:08:42.429 --> 00:08:47.960
digit equal to 3 and the units
digit is equal to 4.

00:08:47.960 --> 00:08:51.190
So it's going to be
like 3 blank 4.

00:08:51.190 --> 00:08:53.410
So how many numbers are here?

00:08:53.410 --> 00:08:57.630
Well, how many digits can
we stick in for that?

00:08:57.630 --> 00:09:01.240
Well, we could put a
0, a 1, 2, 3, 4, 5,

00:09:01.240 --> 00:09:03.940
6, 7, 8, or 9 there.

00:09:03.940 --> 00:09:06.240
We could put any of those
in that middle spot.

00:09:06.240 --> 00:09:09.500
And there are 10 digits we can
put there, so there are 10

00:09:09.500 --> 00:09:10.230
possibilities.

00:09:10.230 --> 00:09:12.640
There are 10 positive three
digit integers that have the

00:09:12.640 --> 00:09:16.060
hundreds digit equal to 3 and
the units digit equal to 4.

00:09:16.060 --> 00:09:17.900
That's choice A.

00:09:17.900 --> 00:09:20.740
That's one of those problems
that you question yourself

00:09:20.740 --> 00:09:23.140
because it seems maybe
even too easy.

00:09:23.140 --> 00:09:25.420
I'll see you in the
next video.


SAT Prep: Test 6 Section 7 Part 2

WEBVTT
Kind: captions
Language: en

00:00:00.890 --> 00:00:03.020
We are on problem number six.

00:00:06.020 --> 00:00:09.760
If there is no waste, how many
square yards of carpeting is

00:00:09.760 --> 00:00:12.960
needed to cover a rectangular
floor that is

00:00:12.960 --> 00:00:15.460
12 feet by 18 feet?

00:00:15.460 --> 00:00:18.700
So I can just draw
it like that.

00:00:18.700 --> 00:00:22.170
And it's 12 feet by 18 feet.

00:00:22.170 --> 00:00:24.660
And the trick here is, they're
not asking how many feet,

00:00:24.660 --> 00:00:28.140
they're asking how many square
yards of carpeting.

00:00:28.140 --> 00:00:30.510
So the easiest thing to do
really at this point, is to

00:00:30.510 --> 00:00:34.640
convert the dimensions
of the room to yards.

00:00:34.640 --> 00:00:37.040
And they tell us 3
feet make a yard.

00:00:37.040 --> 00:00:41.800
So 18 feet, that's the
same thing as what?

00:00:41.800 --> 00:00:44.720
Divide by 3, and you get,
that's 6 yards.

00:00:44.720 --> 00:00:47.020
6 yards is 18 feet.

00:00:47.020 --> 00:00:50.500
And you divide by 3,
you get 4 yards.

00:00:50.500 --> 00:00:52.860
I always find the arithmetic
the hardest part.

00:00:52.860 --> 00:00:54.530
4 yards is equal to
12 feet, right?

00:00:54.530 --> 00:00:56.500
4 times 3 is equal to 12.

00:00:56.500 --> 00:01:02.090
So now this is a 6 by 4, so 6
yards times 4 yards is equal

00:01:02.090 --> 00:01:05.129
to 24 square yards.

00:01:05.129 --> 00:01:07.740
That's choice C.

00:01:07.740 --> 00:01:09.940
And the mistake, if you got
this wrong, you might have

00:01:09.940 --> 00:01:12.610
just-- well one, you might have
multiplied 12 times 18

00:01:12.610 --> 00:01:15.520
and gotten a very large
number and said,

00:01:15.520 --> 00:01:16.180
oh, that's the answer.

00:01:16.180 --> 00:01:17.820
But then your answer would've
been in feet.

00:01:17.820 --> 00:01:19.910
Then the other mistake you might
have done is you might

00:01:19.910 --> 00:01:22.550
have multiplied 12 times 18--
you might done this, 12 times

00:01:22.550 --> 00:01:26.270
18 divided by 3.

00:01:26.270 --> 00:01:28.100
Because you said, oh well, 3
feet is equal to a yard.

00:01:28.100 --> 00:01:31.860
And that is a mistake because
you're now converting square

00:01:31.860 --> 00:01:34.150
feet to square yards.

00:01:34.150 --> 00:01:38.790
And it's actually-- you should
have divided by 9 because

00:01:38.790 --> 00:01:42.410
there's actually 9 square
feet per square yard.

00:01:42.410 --> 00:01:43.090
Why is that?

00:01:43.090 --> 00:01:46.560
Because if I had-- let's
say this is a 1

00:01:46.560 --> 00:01:48.060
square yard, right?

00:01:48.060 --> 00:01:49.700
That means it's going to be
3 feet on that side, 3

00:01:49.700 --> 00:01:50.490
feet on that side.

00:01:50.490 --> 00:01:53.640
So it's actually
9 square feet.

00:01:53.640 --> 00:01:56.770
So if you figured out the area
in feet first, you had to

00:01:56.770 --> 00:01:59.450
divide by 9, not by 3.

00:01:59.450 --> 00:02:02.630
That probably was the most
common mistake, assuming that

00:02:02.630 --> 00:02:04.640
you realized that you had
to convert units.

00:02:04.640 --> 00:02:05.890
Next problem.

00:02:08.289 --> 00:02:10.990
Problem seven.

00:02:10.990 --> 00:02:13.550
A certain scale only registers
weights that are

00:02:13.550 --> 00:02:15.290
greater than 6 pounds.

00:02:15.290 --> 00:02:16.540
OK, fair enough.

00:02:16.540 --> 00:02:18.680
A person who wanted to know
the weights of a puppy, a

00:02:18.680 --> 00:02:22.210
kitten and a bunny-- very cute--
weighed them in pairs

00:02:22.210 --> 00:02:24.720
and got the following results.

00:02:24.720 --> 00:02:27.010
Kitten plus bunny weighed
7 pounds.

00:02:31.090 --> 00:02:33.376
Kitten plus puppy is 8.

00:02:37.290 --> 00:02:39.230
And bunny plus puppy is 9.

00:02:43.490 --> 00:02:46.700
This is by far the cutest
problem I've ever done.

00:02:46.700 --> 00:02:48.640
What is the weight
of the puppy?

00:02:48.640 --> 00:02:53.180
So we want to solve for P.

00:02:53.180 --> 00:02:55.460
Well, if we're going to solve
for P, the best thing we could

00:02:55.460 --> 00:02:59.730
do is we want to use these
two equations.

00:02:59.730 --> 00:03:02.350
But we have three-- if we just
look at these two equations,

00:03:02.350 --> 00:03:04.780
we have three unknowns
with two equations.

00:03:04.780 --> 00:03:10.460
So let's use this equation to
substitute into this equation.

00:03:10.460 --> 00:03:12.370
So let's say we want
to replace this K.

00:03:12.370 --> 00:03:15.970
So we can use this top equation
to say that K is

00:03:15.970 --> 00:03:19.240
equal to 7 minus B.

00:03:19.240 --> 00:03:23.530
So if we substitute that into
this equation, we'll get-- so

00:03:23.530 --> 00:03:28.720
let me just-- this is 7 minus
B, so we'll get 7 minus B--

00:03:28.720 --> 00:03:33.600
and I'm just rewriting this top
equation, that's this--

00:03:33.600 --> 00:03:36.850
plus P is equal to 8.

00:03:36.850 --> 00:03:42.480
And then this bottom equation
still is B plus

00:03:42.480 --> 00:03:44.450
P is equal to 9.

00:03:44.450 --> 00:03:47.410
I could add the 7 or subtract
7 from both sides right now,

00:03:47.410 --> 00:03:49.900
but I'm just going to actually
add the equations, because I

00:03:49.900 --> 00:03:51.090
like how these B's are
going to cancel out.

00:03:51.090 --> 00:03:53.820
I get excited about canceling
variables.

00:03:53.820 --> 00:03:57.000
So-- actually, no let me
subtract 7 from both sides

00:03:57.000 --> 00:03:59.900
first. So if we take 7 from
here, than this 8

00:03:59.900 --> 00:04:00.860
becomes a 1, right?

00:04:00.860 --> 00:04:02.760
I just subtracted 7
from both sides.

00:04:02.760 --> 00:04:05.740
So negative B plus
P is equal to 1.

00:04:05.740 --> 00:04:07.420
Now I just add these
two equations.

00:04:07.420 --> 00:04:08.550
And what's minus B plus B?

00:04:08.550 --> 00:04:14.680
It's 0 plus P plus P is 2P is
equal to 1 plus 9 is 10.

00:04:14.680 --> 00:04:16.100
2P equals 10.

00:04:16.100 --> 00:04:17.950
P is equal to 5.

00:04:17.950 --> 00:04:18.730
Choice D.

00:04:18.730 --> 00:04:22.530
5 pounds, that's how much
the puppy weighs.

00:04:22.530 --> 00:04:25.430
Which shows us the bunny weighs
2 pounds, and the

00:04:25.430 --> 00:04:26.450
kitten weighs 3 pounds.

00:04:26.450 --> 00:04:29.520
Which is-- it looks like they
actually thought about how

00:04:29.520 --> 00:04:32.450
much a puppy, a bunny and a
kitten would actually weigh,

00:04:32.450 --> 00:04:34.960
which I have to give
them credit for.

00:04:34.960 --> 00:04:37.570
Next problem.

00:04:37.570 --> 00:04:40.520
Problem eight.

00:04:40.520 --> 00:04:47.490
On a blueprint, 1/4
inch represents 16

00:04:47.490 --> 00:04:49.730
feet in real life.

00:04:49.730 --> 00:04:53.510
If a driveway is 40 feet long,
what is its length in inches

00:04:53.510 --> 00:04:54.890
on the map?

00:04:54.890 --> 00:04:59.850
So a driveway-- that's a
driveway, I don't know, that's

00:04:59.850 --> 00:05:01.260
my driveway.

00:05:01.260 --> 00:05:07.890
And it's 40 feet long.

00:05:07.890 --> 00:05:10.460
So how many of these units
is it going to be?

00:05:14.720 --> 00:05:18.880
Well, actually-- we could do it
a bunch of different ways.

00:05:18.880 --> 00:05:22.530
We could say 1/4 of an inch
is equal to 16 feet.

00:05:22.530 --> 00:05:25.500
If we multiply both sides of
this relationship by 4, you

00:05:25.500 --> 00:05:31.910
get 1 inch is equal
to 64 feet.

00:05:31.910 --> 00:05:34.226
1 inch-- I just multiplied
both sides of this

00:05:34.226 --> 00:05:35.930
relationship by 4.

00:05:35.930 --> 00:05:38.930
So if you want to figure out
how many inches this would

00:05:38.930 --> 00:05:42.640
represent, you would say, well,
x is how many inches it

00:05:42.640 --> 00:05:48.730
would represent over 1 inch
is equal to this length,

00:05:48.730 --> 00:05:52.050
40 feet, over 64.

00:05:52.050 --> 00:05:53.790
It's the same fraction.

00:05:53.790 --> 00:05:59.360
And of course, if you divide
by 1, this cancels out.

00:05:59.360 --> 00:06:02.250
So you're left with x, which
is its representation in

00:06:02.250 --> 00:06:05.950
inches, is equal to 40/64.

00:06:05.950 --> 00:06:10.020
Well you could divide the top
and the bottom by 8, so that

00:06:10.020 --> 00:06:12.880
becomes 5/8.

00:06:12.880 --> 00:06:14.220
40 divided by 5.

00:06:14.220 --> 00:06:15.840
64 divided by 8.

00:06:15.840 --> 00:06:18.140
x is equal to 5/8.

00:06:18.140 --> 00:06:20.970
And that is choice B.

00:06:20.970 --> 00:06:21.820
Next problem.

00:06:21.820 --> 00:06:22.900
There's a bunch of ways you
could have don e it.

00:06:22.900 --> 00:06:27.090
This is the way that
occurred to me.

00:06:27.090 --> 00:06:31.590
Next problem, problem nine.

00:06:31.590 --> 00:06:36.140
In the xy-coordinate system, p
comma 0 is one of the points

00:06:36.140 --> 00:06:38.840
of intersection of the graphs--
OK, so they're giving

00:06:38.840 --> 00:06:40.150
us two graphs.

00:06:40.150 --> 00:06:45.360
y is equal to minus x squared
plus 9, and the other graph is

00:06:45.360 --> 00:06:51.120
y is equal to x squared
minus 9.

00:06:51.120 --> 00:06:58.950
If p is positive, what
is the value of p?

00:06:58.950 --> 00:07:00.360
So they're saying that the
coordinate where they

00:07:00.360 --> 00:07:03.970
intersect is p comma 0.

00:07:03.970 --> 00:07:05.115
So we want to figure out the

00:07:05.115 --> 00:07:10.320
x-coordinate where they intersect.

00:07:10.320 --> 00:07:13.650
So the easy way-- you know,
they're tempting you to add

00:07:13.650 --> 00:07:16.090
these equations and do all sorts
of things, but we know

00:07:16.090 --> 00:07:19.260
that they intersect at the
point y is equal to 0.

00:07:19.260 --> 00:07:21.050
They're telling us that, so we
don't have to do all this

00:07:21.050 --> 00:07:21.590
fancy stuff.

00:07:21.590 --> 00:07:23.470
We don't have to figure out
where they intersect.

00:07:23.470 --> 00:07:25.060
They tell us it intersects
at y equals 0.

00:07:25.060 --> 00:07:29.190
So y equals 0, what's x in
either of these situations?

00:07:29.190 --> 00:07:31.030
Well, let's take this
second equation.

00:07:31.030 --> 00:07:34.020
0 is equal to x squared
minus 9.

00:07:34.020 --> 00:07:38.280
Add 9 to both sides, you get
x squared is equal to 9.

00:07:38.280 --> 00:07:41.400
I added 9 and switched
the sides.

00:07:41.400 --> 00:07:44.680
You get x is equal to
plus or minus 3.

00:07:44.680 --> 00:07:48.350
And they tell us, that if
p is positive, what is

00:07:48.350 --> 00:07:49.530
the value of p?

00:07:49.530 --> 00:07:52.180
Well, it has to be
plus 3 then.

00:07:52.180 --> 00:07:55.160
And that is choice A.

00:07:55.160 --> 00:07:56.390
And you could have used
the top equation.

00:07:56.390 --> 00:08:00.390
You could have said 0 is equal
to negative x squared plus 9.

00:08:00.390 --> 00:08:01.200
You would've gotten
the same thing.

00:08:01.200 --> 00:08:03.600
You would've gotten x squared
is equal to 9, x is equal to

00:08:03.600 --> 00:08:05.120
plus or minus 3.

00:08:05.120 --> 00:08:08.080
You would've gotten the
same thing either way.

00:08:08.080 --> 00:08:09.150
Next problem.

00:08:09.150 --> 00:08:10.053
I don't know if I'm going
to have time to

00:08:10.053 --> 00:08:10.840
do it in this video.

00:08:10.840 --> 00:08:13.930
I might have to do
it in the next.

00:08:13.930 --> 00:08:16.370
Problem ten.

00:08:16.370 --> 00:08:19.540
The Smith Metal Company's
old machine makes

00:08:19.540 --> 00:08:21.100
300 bolts per hour.

00:08:21.100 --> 00:08:24.610
300-- I'll call it b per h.

00:08:24.610 --> 00:08:30.220
Its new machine makes
450 bolts per hour.

00:08:30.220 --> 00:08:34.890
If both machines begin running
at the same time, how many

00:08:34.890 --> 00:08:38.880
minutes will it take the
two machines to make a

00:08:38.880 --> 00:08:41.539
total of 900 bolts?

00:08:41.539 --> 00:08:42.220
So how many minutes?

00:08:42.220 --> 00:08:44.120
So let's say m for minutes.

00:08:44.120 --> 00:08:46.480
So the total number of bolts
they're going to produce-- so

00:08:46.480 --> 00:08:56.380
bolts is going to be equal--
so this is per hour, right?

00:08:56.380 --> 00:08:57.790
These are both per hour.

00:08:57.790 --> 00:09:01.400
So let's figure it out minutes,
because they're

00:09:01.400 --> 00:09:03.420
asking us how many minutes
will it take.

00:09:03.420 --> 00:09:06.860
So if you make 300 bolts in an
hour, you're going to make

00:09:06.860 --> 00:09:08.740
1/60 that in a minute.

00:09:08.740 --> 00:09:11.920
So what's 1/60 of 300?

00:09:11.920 --> 00:09:16.910
Well, 300 divided by 60
is 5 bolts per minute.

00:09:16.910 --> 00:09:23.390
And this one-- what's
450 divided by 60?

00:09:23.390 --> 00:09:24.340
Actually, I'm going to
run out of time.

00:09:24.340 --> 00:09:25.590
I'm going to do this problem
in the next video.

00:09:25.590 --> 00:09:27.320
I'll see you soon.