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John and Marry were each paid x dollars in advance to do a [#permalink]

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07 Jun 2008, 13:59

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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?

Re: PS: OG (11) - #220 - Please solve [#permalink]

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07 Jun 2008, 14:14

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vksunder wrote:

John and Marry 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

Thanks!

we know that both J and M worked a total of 18 hours They each got paid x dollars. Total money paid out therefore is 2x

therefore the hourly wage is 2x/18 = x/9

now John worked 10 hours, but got paid x (for 9 hours), so Mary paid him y for the extra 1 hour to equilise their payments

Re: PS: OG (11) - #220 - Please solve [#permalink]

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07 Jun 2008, 14:39

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vksunder wrote:

How did you come up with 9 hours -- now John worked 10 hours, but got paid x (for 9 hours),

Thanks for your input.

basically the stem says that John worked for 10 hours out of a total of 18. So Mary worked for 8. BUT they both got paid evenly. Mary (because she is so nice ) decide to give John some money to equalise their pay so if she gives John 1 hour's worth of pay, since he has been paid 9 hours worth in advanced ($x), this will equalise the pay.

Re: PS: OG (11) - #220 - Please solve [#permalink]

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07 Jun 2008, 14:45

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[quote="vksunder"]John and Marry 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

Let $x be the advance that both receive = 2x Amount earned per hour by John and Mary = x/10 and x/8 Mary gives $y to John to make the wages earned equal Hence John wage per hr = (x+y)10 which is now equal to Mary's wage (x-y)/8 Solve (x+y)10 = (x-y)/8 8x + 8y = 10x -10y 2x = 18y x = 9y Ans. E

Re: PS: OG (11) - #220 - Please solve [#permalink]

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07 Jun 2008, 19:53

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The way I figured it was substituting numbers.

John works 10 hours, Mary 8. So total of 18 hours. I did this.

They each get $90, so total of $180. That's $9 / hr for john and $11.25 for Mary. It's easier to figure out with $180 and 18 hours, they should each get $10 / hr. So if John has $90 and needs $100 to give him $10/hr, then Mary gives him $10, which is y. The question says "In terms of y, how much did John get to begin with?" Well that's \(\frac{90}{10}y\)

vksunder wrote:

Have anyone of you tried to solve this problem MGMAT way. That is, by substituting #'s

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: PS: OG (11) - #220 - Please solve [#permalink]

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08 Jun 2008, 10:30

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vksunder wrote:

John and Marry 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.

Re: John and Marry were each paid x dollars in advance to do a [#permalink]

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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

The amount Mary has in the end is x-y dollars and she worked for 8 hours; The amount John has in the end is x+y dollars and he worked for 10 hours;;

We are told that in this case their hourly wage was the same: \(hourly \ wage=\frac{wage}{# \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10}\), from \(\frac{x-y}{8}=\frac{x+y}{10}\) we get that \(x=9y\).

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