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SHAFTBMF
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Post subject: Official Guide #220  Posted: Thu Sep 13, 2007 1:49 am |
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What is the approach for this? I found myself initally thinking I could easily do it. then flailing around.
Again, the use of in terms of y is always confusing for me...
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
thank you.
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shaftbmf
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Post subject: Correction..this is official guide problem #220 Posted: Thu Sep 13, 2007 1:58 am |
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Correction..this is official guide problem #220..THANKS
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StaceyKoprince
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Post subject: Posted: Thu Sep 13, 2007 5:07 pm |
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| ManhattanGMAT Staff |
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Posts: 6077
Location: San Francisco
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Classic Word Translations - just have to be VERY careful as you write the equation. John worked for 10 hours; Mary worked for 8. They were each paid the same amount (x) to do this job, so Mary's hourly wage is x/8 and John's is x/10. Mary gave John y dollars of her payment and, after that, their hourly wage was equal. That last bit is very important - equal means I can write an equation.
So, instead of making x dollars each, Mary makes x-y dollars and John makes x+y dollars. The hourly wage is still $/h, or (x-y)/8 for Mary and (x+y)/10 for John. These two amounts are equal:
(x-y)/8 = (x+y)/10 cross-multiply
10x - 10y = 8x + 8y simplify
2x = 18y
Now the "x in terms of y" language is always confusing, but look at your answers - they all contain y. So I know I should solve my equation for x.
2x = 18y
x = 9y
E
_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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davetzulin
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Post subject: Re: Official Guide #220 Posted: Wed Apr 25, 2012 9:55 pm |
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i have another way I think is easier, though perhaps not as elegant.
the idea of "wage" or money/time is a difficult conceptual stretch for me, especially when pressed for time.
given: John worked 10 hours
given: Mary worked 8 hours
easy conclusion: the total hours worked = 18 hours
easy conclusion: the total amount paid to both = 2x (each paid x)
but,
john worked 10/18 of the time
mary worked 8/18 of the time
to be fair, john should get 10/18 * 2x of the money
(and mary should get 8/18 * 2x of the money )
therefore john should get 20x/18 of the money,
but john got x only!
so x + y = 20x/18 where y is the amount that mary gave to john to get everyone equal
solve:
18x + 18y = 20x
2x = 18y
x = 9y
you can do the same thing with Mary and arrive at the same answer
x - y = 8/18 *2x
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jnelson0612
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Post subject: Re: Official Guide #220 Posted: Mon Apr 30, 2012 11:36 pm |
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Posts: 1857
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Dave, that is seriously sweet! Love your approach! I'm writing that down right now in my OG. :-) Thanks for posting!
_________________
Jamie Nelson
ManhattanGMAT Instructor
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