Peter and Mary earn a total of $502 by working a total of 37 hours. If Peter earns $16/h and Mary earns $10/h, how many hours did each work?
A) Peter worked 19 hours and Mary worked 19 hours.
B) Mary worked 15 hours and Peter worked 22 hours.
C) Peter worked 24 hours and Mary worked 13 hours.
D) Peter worked 22 hours and Mary worked 15 hours.
E) Peter worked 19 hours and Mary worked 18 hours.

Question

Quizplus · Accepted Answer

Let's use algebra to solve the problem. Let x be the number of hours Peter worked and y be the number of hours Mary worked. Then we have two equations:

x + y = 37 (total number of hours worked)
16x + 10y = 502 (total amount earned)

We can simplify the first equation to get:

y = 37 - x

Substitute this into the second equation to get:

16x + 10(37 - x) = 502
Simplify and solve for x:
6x + 370 = 502
6x = 132
x = 22

Substitute x = 22 back into y = 37 - x to get:

y = 15

Therefore, Peter worked 22 hours and Mary worked 15 hours. The answer is D.

Peter and Mary Earn a Total of $502 by Working