1. ## algebra

4. Mr Benny is now 3 times as old as his son. In 13 years time, he will be twice as old as his son. Find Mr Benny's present age.

5. the sum of the present ages of Mrs Peel and her daughter Emma is 50 years. In 5 years tiME Mrs Peel will be 3 times as old as Emma. How old is Emma now?

2. Originally Posted by alberta
4. Mr Benny is now 3 times as old as his son. In 13 years time, he will be twice as old as his son. Find Mr Benny's present age.
Let the son's age be x. Then Mr. Benny's age is currently 3x. In 13 years, the son's age is x + 13 and Mr. Benny's age is 3x + 13. The problem says that Mr. Benny's age in 13 years is twice his son's age in 13 years, so:
3x + 13 = 2(x + 13)

And now solve for x. (I got x = 13, so Mr. Benny's age present age is 3*13 = 39.)

-Dan

3. Originally Posted by alberta
5. the sum of the present ages of Mrs Peel and her daughter Emma is 50 years. In 5 years tiME Mrs Peel will be 3 times as old as Emma. How old is Emma now?
Try this the same way as I set up the last one. Call Emma's age x. What is Mrs Peel's age right now? What is Emma's age in 5 years? What is Mrs Peel's age in 5 years? Use this to set up the second sentence as an equation. If you need more help, just let us know. (Note: I got x = 10.)

-Dan

4. Hello, Alberta!

For years, I used a chart to organize the information.
I'll do the first one . . .

4. Mr. Benny is now 3 times as old as his son.
In 13 years time, he will be twice as old as his son.
Find Mr. Benny's present age.

In the chart, make a row for each person.
Code:
- - - - - + - - - - - - - -
Mr. Benny |
- - - - - + - - - - - - - -
son    |
- - - - - + - - - - - - - -

Make a column for each time period: "Now" and some other time.
Code:
          | Now | +13 yrs |
- - - - - + - - + - - - - +
Mr. Benny |     |         |
- - - - - + - - + - - - - +
son    |     |         |
- - - - - + - - + - - - - +

Mr. Benny is 3 times his son's age.
. . Let $x$ = son's age (now).
. . Let $3x$ = Mr. Benny's age (now)
Write those in the "Now" column.
Code:
          | Now | +13 yrs |
- - - - - + - - + - - - - +
Mr. Benny | 3x  |         |
- - - - - + - - + - - - - +
son    |  x  |         |
- - - - - + - - + - - - - +

13 years in the future, both will be 13 years older.
. . Mr. Benny will be $3x + 13$ years old.
. . His son will be $x + 13$ years old.
Write those in the "+13 years" column.
Code:
          | Now | +13 yrs |
- - - - - + - - + - - - - +
Mr. Benny | 3x  | 3x + 13 |
- - - - - + - - + - - - - +
son    |  x  |  x + 13 |
- - - - - + - - + - - - - +

Our equation come from the second column.

In 13 years: . $\underbrace{\text{Mr. Benny}}_\downarrow \:\underbrace{\text{will be}}_\downarrow\: \underbrace{\text{twice}}_\downarrow\:\underbrace{ \text{son's age}}_\downarrow$
. . . . . . . . . . . $3x + 13\quad\;\; = \quad\;\;\: 2 \:\times \;(x + 13)$

And there is our equation!

Solve for $x$, but don't forget:
. . they asked for Mr. Benny's age $(3x)$.

5. Neat idea. I'll have to remember that!

-Dan

6. i neva saw how easy it woz..it took me all day...thanx 2 both of yall
-chart is a good idea-