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

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01 May 2009, 01:52

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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?

Can you all please walk me thru OG #204 in the PS section. The explanation in the book was rather succinct. Thanks!

"John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job 20 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?"

Can you all please walk me thru OG #204 in the PS section. The explanation in the book was rather succinct. Thanks!

"John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job 20 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 and Mary each received x dollars. If Mary gave y dollars to John, the dollar amount Mary retained was x - y and the dollar amount John got was x + y. Now, the important concept here is that if they received the same hourly wage, these amounts should be in the same ratio as the time for which they worked. (Think of it this way: Two people get $50/hr. One works for 10 hrs and so gets $500. Other works for 11 hrs and gets $550. The amount they earned will be in the ratio 500/550 = 10/11)

So \(\frac{(x - y)}{(x + y)} = \frac{18}{20}\) Cross multiply to get x = 19y

The question actually has "John worked for 10 hours", not 20 and hence you get the answer x = 9y (E).
_________________

I think that this is a relatively easy question from OG. Obviously there is an explanation which uses system of equations, however I am trying to work this question using substitution and can't reach correct solution What am I doing wrong?

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 the payment so that they would have received the same hourly wage, what was the dollar mount in terms of y, that John was paid in advance?

4y 5y 6y 8y 9y

If x=100, Mary gave John $20. Which means that his pay was 5y.... However OA is 9y.

I think that this is a relatively easy question from OG. Obviously there is an explanation which uses system of equations, however I am trying to work this question using substitution and can't reach correct solution What am I doing wrong?

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 the payment so that they would have received the same hourly wage, what was the dollar mount in terms of y, that John was paid in advance?

4y 5y 6y 8y 9y

If x=100, Mary gave John $20. Which means that his pay was 5y.... However OA is 9y.

How did you get y=$20 for x=$100?

Anyway below is algebraic approach maybe it helps:

Amount Mary has in the end is x-y dollars and she worked for 8 hours; 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 \(x=9y\).

I think that this is a relatively easy question from OG. Obviously there is an explanation which uses system of equations, however I am trying to work this question using substitution and can't reach correct solution What am I doing wrong?

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 the payment so that they would have received the same hourly wage, what was the dollar mount in terms of y, that John was paid in advance?

4y 5y 6y 8y 9y

If x=100, Mary gave John $20. Which means that his pay was 5y.... However OA is 9y.

So we assume x to be $100. Fair enough. John and Mary received $100 each so in all they received $200. John worked for 10 hrs and Mary worked for 8 hrs so they put in a total of 18 hrs. If their hourly rates are to be the same, they should receive $\(\frac{200}{18} = 11.11\) per hour. So Mary must have received $88.88 finally and John must have received $111.11. That is, Mary gave John $11.11 = y. John was paid an advance of $100 which is equal to 9*11.11 (i.e. 9y) = $100 (approximately since 11.11 is actually 11.111111...)

Note: Mary didn't give John $20 since then she would have had $80 for 8 hrs ($10/hr) and John would have had $120 for 10 hrs ($12/hr).
_________________

Can someone help me chart this problem out please. 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?

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

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27 Sep 2014, 00:25

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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 \(x=9y\).

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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