Suyog 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
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
