As a math professor, you will solve the given problem accurately '<using algebra>'. If there is no exact match choose the closest option.

Question: NAME_1 found that the average of 15 numbers is 40. If 10 is added to each number then the mean of the numbers
Answer Choices: (A) 50 (B) 45 (C) 65 (D) 78 (E) 64
Approach: <using algebra>
Let's denote the sum of the 15 numbers as S. Since the average of the 15 numbers is 40, we can write the equation:
S / 15 = 40
S = 40 * 15 = 600
Now, we add 10 to each number, so the new sum is S + 15 * 10 = 600 + 150 = 750. The new average is:
New average = 750 / 15 = 50
The answer is: (A) 50

Question: If a / b = 3/4 and 8a + 5b = 22,then find the value of a.  
Answer Choices: (A) 1/2 (B) 3/2 (C) 5/2 (D) 4/2 (E) 7/2
Approach: <using algebra>
To solve the given problem, we can use substitution. Since a / b = 3/4, we can write that as:
a = 3b/4
Now, substitute this expression for a into the second equation:
8(3b/4) + 5b = 22
Simplify and solve for b:
6b + 5b = 22
11b = 22
b = 2
Now that we have the value of b, we can find the value of a:
a = 3b/4
a = 3(2)/4
a = 6/4
a = 3/2
So, the value of a is (B) 3/2.
The answer is: (B) 3/2

Question: A person is traveling at 20 km/hr and reached his destiny in 2.5 hr then find the distance?
Answer Choices: (a) 53 km (b) 55 km (c) 52 km (d) 60 km (e) 50 km
Approach: <using algebra>
Using the formula distance = speed × time, we can calculate the distance as follows:
Distance = 20 km/hr × 2.5 hr = 50 km
So, the closest answer choice is (e) 50 km.
The answer is: (e) 50 km

Question: How many keystrokes are needed to type the numbers from 1 to 500?  
Answer Choices: (a) 1156 (b) 1392 (c) 1480 (d) 1562 (e) 1788
Approach: <using algebra>
Let's break down the number of keystrokes needed into groups based on the number of digits:
One-digit numbers (1-9): There are 9 one-digit numbers, so we need 9 keystrokes.
Two-digit numbers (10-99): There are 90 two-digit numbers, each requiring 2 keystrokes, so we need 90 * 2 = 180 keystrokes.
Three-digit numbers (100-500): There are 401 three-digit numbers (500 - 100 + 1), each requiring 3 keystrokes, so we need 401 * 3 = 1203 keystrokes.
Now let's add up the keystrokes from all groups: 9 + 180 + 1203 = 1392.
Therefore, the closest option is (b) 1392.
The answer is: (b) 1392


Question: The original price of an item is discounted 22%. A customer buys the item at this discounted price using a $20-off coupon. There is no tax on the item, and this was the only item the customer bought. If the customer paid $1.90 more than ha