LUANDATO wrote:John and Mary were 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

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 = E

Cheers,
Brent

LUANDATO wrote:John and Mary were 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

The OA is E.

I'm really confused by this PS question. Experts, any suggestion?

I tried to solve it as follow,

x/10 johns wage
x/8 mary wage

x/8-y=x/10+y

x= 80y

80y/10= 8y so my answer was D.

However, it is wrong. I don't get it. Where is the mistake? I need your help, please! Thanks in advance.

The problem with your solution is highlighted above in green

In order for their hourly wages to be the same, we need (x - y)/8 = (x + y)/10
We need this because hourly wage = (total $ received)/(total hours worked)

For more on this, see my solution below.

Cheers,
Brent

LUANDATO wrote:John and Mary were 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. So we can say:

John's hours = 10

Mary's hours = 8

We are also given that John and Mary were each given x dollars in advance. We can use this to determine the hourly wage for both Mary and John.

Since (hourly wage)(# of hours) = total paid, we can say that:

hourly wage = (total paid)/(# of hours)

John's hourly wage = x/10

Mary's hourly wage = x/8

We are also told that Mary gave John y dollars of her payment so that they would have an equal hourly wage. This means that Mary actually made (x - y) dollars. Since John received y dollars he now makes (x + y) dollars. Using this information, the revised hourly wages of John and Mary are:

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 revised hourly wages of John and Mary equal to each other.

(x + y)/10 = (x - y)/8

We cross multiply and obtain:

8x + 8y = 10x - 10y

-2x = -18y

x = 9y

Answer: E