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John and Mary were each paid x dollars in advance to do a certain job

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: john-and-mary-were-each-paid-x-dollars-in-advance-to-do-a-144782.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Sep 2014, 00:49, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: John and Mary were each paid x dollars in advance to do a certain job [#permalink]

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New post 01 May 2009, 06:48
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Ans is (A) 4y

Here is how I got

John worked for = 10 hr
Mary worked for = 8 hr (2 less than John)

Advance payment to John and Mary = x dollars
Mary gave John so that they have equal pay per hour = y dollars

This means their per hour amount is equal.

x/10 = (x-y)/8

Calculating this gives x = 5y. Reducing the extra y given by Mary to John gives 4y
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Re: John and Mary were each paid x dollars in advance to do a certain job [#permalink]

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New post 01 May 2009, 08:14
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i got E 9y
Here is how I got

John worked for = 10 hr
Mary worked for = 8 hr (2 less than John)

Advance payment to John and Mary = x dollars
Mary gave John y dollars so that they have equal pay per hour

This means their per hour amount is equal.
so mary now have x-y and john now have x+y
so (x-y)/8 = (x+y)/10

which gives x =9y
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Re: John and Mary were each paid x dollars in advance to do a certain job [#permalink]

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New post 01 May 2009, 09:13
aharonm wrote:
i got E 9y


You are right, I missed adding the y to John payment.
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#204 OG PS [#permalink]

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Hello,

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
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Re: #204 OG PS [#permalink]

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New post 23 Nov 2010, 17:42
tonebeeze wrote:
Hello,

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).
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Re: #204 OG PS [#permalink]

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New post 23 Nov 2010, 21:41
The options are wrong or there is a prob with the question....???
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Re: #204 OG PS [#permalink]

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New post 24 Nov 2010, 07:47
punetpratik - the question was written wrong. It should have said John worked for 10 hours.
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Re: #204 OG PS [#permalink]

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New post 24 Nov 2010, 07:54
i kept getting 19y. i thought i was losing my mind for a sec until i read the top post by VeritasPrepKarishma . Thanks for pointing it out.
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Problem from OG [#permalink]

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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 :roll: 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.
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Re: Problem from OG [#permalink]

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vasili wrote:
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 :roll: 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 \(x=9y\).

Answer: E.
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Re: Problem from OG [#permalink]

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vasili wrote:
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 :roll: 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).
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OG PS #204 [#permalink]

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New post 28 Dec 2010, 16:59
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?

(A) 4y
(B) 5y
(C) 6y
(D) 8y
(E) 9y
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Re: OG PS #204 [#permalink]

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Re: Problem from OG [#permalink]

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New post 28 Dec 2010, 21:00
Bunuel - You mentioned "merging similar topics", but i don't see the links to similar topics. Where do I see similar topics. Please advice

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

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

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milind1979 wrote:
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 \(x=9y\).

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: john-and-mary-were-each-paid-x-dollars-in-advance-to-do-a-144782.html
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Re: Problem from OG [#permalink]

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Re: #204 OG PS [#permalink]

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Re: #204 OG PS   [#permalink] 17 May 2016, 18:36
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