John and Mary - Applied problem

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John and Mary - Applied problem

by anirudhbhalotia » Thu Mar 10, 2011 9:21 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

OA - E
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by srcc25anu » Thu Mar 10, 2011 11:19 am
each be paid = x therefore total payment = 2x
their respective speed has to be equal to get the same hourly wage

M is paid hourly wage of x/8
J is paid an hourly wage of x/10

x/8 > x/10

therefore [ total payment to m (x) - amount she pays to M (y) ] / hours worked = equal to average pay per hour (i.e. total pay of 2x dividd by total hours of work i.e. 18 hours)

so (x-y) / 8 = 2x / 18
or x-y / 8 = x / 9

Solving we get:
9x - 9y = 8x
x=9y

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by GMATGuruNY » Thu Mar 10, 2011 11:28 am
anirudhbhalotia 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

OA - E
We can plug in values that satisfy the conditions given.

Let wage = $2/hr.

John works 10 hours. He should earn 10*2 = $20.
Mary works 8 hours. She should earn 8*2 = $16.
The total earned is 20+16 = $36.
So each was paid in advance x = $18.
For John to earn $20, Mary must give John y = $2.

John was paid in advance $18. This is our target.

Now we plug y=2 into the answers to see which yields our target of 18.

Only answer choice E works:
9y = 9*2 = $18.

The correct answer is E.

Hope this helps!
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