OG PS #204 VIC problem

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tonebeeze: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Nov 02, 2009 5:49 pmFollowed by: 3 members; Thanked: 2 times

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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Source: Beat The GMAT — Problem Solving | Tue Dec 28, 2010 5:11 pm

anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

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

(Every mistake is a lesson learned )

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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 » 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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