Hourly Wage

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RiyaR: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Sat May 31, 2014 8:29 pmFollowed by: 2 members; Thanked: 1 times

by RiyaR » Wed Sep 24, 2014 7:52 am

. 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

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Source: Beat The GMAT — Problem Solving | Wed Sep 24, 2014 7:52 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Sep 24, 2014 7:58 am

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 can plug in a value for the hourly rate.

Let hourly rate = $1.
Since John works 10 hours, he earns 10*1 = $10.
Since Mary works 10-2=8 hours, she earns 8*1 = $8.
Thus, the total advance payment to John and Mary = 10+8 = $18.
Since each receives x dollars in advance, x = 18/2 = $9.

John is given x=9 in advance but must earn $10.
Mary is given x=9 in advance but must earn $8.
Thus, Mary gives John y=1.

The question asks for the amount that John is paid in advance: $9.
This is our target.
Now we plug y=1 into the answers to see which yields our target of 9.

Only answer choice E works:
9y = 9*1 = 9.

The correct answer is E.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Sep 24, 2014 9:45 am

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

Another 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 = [spoiler]x = 9y = E[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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