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

One approach:

Salary
Mary's NET salary was x - y dollars (because Mary gave John y dollars)
John's NET salary was x + y dollars

Hours worked
Mary worked 8 hours
John worked 10 hours


In the end, John and Mary received the SAME hourly wage.
So, John's hourly wage = Mary's hourly wage
Hourly wage = (total salary)/(hours worked)
So, (x + y)/10 = (x - y)/8

In terms of y, that John was paid in advance?
In other words, what is the value of x (in terms of y)
So, we'll solve our equation for x.

Take (x + y)/10 = (x - y)/8 and cross multiply to get:
10(x - y) = 8(x + y)
Expand: 10x - 10y = 8x + 8y
Rearrange: 2x = 18y
Divide by 2: x = 9y
So, John's advance payment = x = 9y

Answer: E

Cheers,
Brent

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