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OG PS #204 VIC problem

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OG PS #204 VIC problem

by tonebeeze » Tue Dec 28, 2010 5:11 pm
Can someone help me chart this problem out please. I'm having trouble with this one. Is it better to use the plug in method or algebra? Thanks.

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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by anshumishra » Tue Dec 28, 2010 5:56 pm
tonebeeze wrote:Can someone help me chart this problem out please. I'm having trouble with this one. Is it better to use the plug in method or algebra? Thanks.

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

John -> Received x dollars
Mary -> Received x dollars

After Mary gave y dollars to John;

John -> has x+y dollars -> worked for 10 hrs
Mary -> has x-y dollars -> worked for 8 hrs

Now since their hourly wage is same => (x+y)/10 = (x-y)/8
=> 2x/2y = (10+8)/(10-8) = 9
=> x = 9y.

E.
Thanks
Anshu

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by GMATGuruNY » Tue Dec 28, 2010 6:21 pm
tonebeeze wrote:Can someone help me chart this problem out please. I'm having trouble with this one. Is it better to use the plug in method or algebra? Thanks.

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
John works for 10 hours and Mary works for 8 hours.
Let's plug in for the hourly wage. Let wage = 10.

John's pay = 10*10 = 100.
Mary's pay = 8*10 = 80.
Combined pay = 100+80 = 180.
Since John and Mary were each given x dollars in advance, x = 180/2 = 90.
Since Mary was given $90 in advance and her final pay was $80, Mary gave John $10. So y=10.
The problem asks for the amount that John was paid in advance: $90. This is our target answer.

Now we plug y=10 into the answer choices to see which yields our target of 90.

Only answer choice E works:
9y = 9*10 = 90.

The correct answer is E.
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