M7MBA wrote:John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?
(A) 4y
(B) 5y
(C) 6y
(D) 8y
(E) 9y
[spoiler]OA=E[/spoiler]
Source: Official Guide
We are first given that John worked for 10 hours and that Mary worked for 2 hours less than John. It follows that:
John's hours = 10
Mary's hours = 8
We are also given that John and Mary were each given x dollars in advance. We are also told that Mary gave John y dollars of her payment so that they would have an equal hourly wage. It follows that Mary actually made (x - y) dollars. Since John received y dollars from Mary, he now made (x + y) dollars. Using this information, the hourly wages of John and Mary are:
hourly wage = (total paid) / (# of hours)
Mary's wage = (x - y) / 8
John's wage = (x + y) / 10
Since we are told that the two hourly wages are the same, we can set the hourly wages of John and Mary equal to each other.
(x + y) / 10 = (x - y) / 8
We can cross multiply and solve:
8x + 8y = 10x - 10y
-2x = -18y
x = 9y
Answer: E
