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

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

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New post 04 May 2016, 09:33
Walkabout 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


We are first given that John worked for 10 hours and that Mary worked for 2 hours less than John. So we can say:

John’s hours = 10

Mary’s hours = 8

We are also given that John and Mary were each given x dollars in advance. We can use this to determine the hourly wage for both Mary and John.

Since (hourly wage)(# of hours) = total paid, we can say that:

hourly wage = (total paid)/(# of hours)

John’s hourly wage = x/10

Mary’s hourly wage = x/8

We are also told that Mary gave John y dollars of her payment so that they would have an equal hourly wage. This means that Mary actually made x – y dollars. Since John received y dollars he now makes x + y dollars. Using this information, the hourly wages of John and Mary are:

Mary’s wage = (x – y)/8

John’s wage = (x + y)/10

Since we are told that the two hourly wages are the same, we can set the hourly wages of John and Mary equal to each other.

(x + y)/10 = (x – y)/8

We can cross multiply and we get:

8x + 8y = 10x – 10y

-2x = -18y

x = 9y

Answer is E.
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 04 May 2016, 09:42
Walkabout 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


Hi,
A simple way to look at the problem is ..
they were paid x for equal hours..
so the time was supposed to be\(\frac{10+8}{2} = 9\) hr..
M gives y dollar to J since she worked one hour less and J worked 1 hr more than 9.. so hourly wage is y..
for 9 hours wage = 9y = x

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

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New post 01 May 2017, 05:56
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Top Contributor
Walkabout 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


Salary
Mary's NET salary was x - y dollars (because Mary gave John y dollars)
John's NET salary was x + y dollars

Hours worked
Mary worked 8 hours
John worked 10 hours


In the end, John and Mary received the SAME hourly wage.
So, John's hourly wage = Mary's hourly wage
Hourly wage = (total salary)/(hours worked)
So, (x + y)/10 = (x - y)/8

In terms of y, that John was paid in advance?
In other words, what is the value of x (in terms of y)
So, we'll solve our equation for x.

Take (x + y)/10 = (x - y)/8 and cross multiply to get:
10(x - y) = 8(x + y)
Expand: 10x - 10y = 8x + 8y
Rearrange: 2x = 18y
Divide by 2: x = 9y
So, John's advance payment = x = 9y = E

Cheers,
Brent
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 03 May 2017, 14:47
average hourly wage= total wage/hour worked
(advance+y)/10 = (advance-y)/8
advance=9y
answer:E
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John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post Updated on: 15 May 2018, 14:18
They each received the same payment in advance. Pick a random #: say $20.

John worked 10 hours and Mary worked 10 - 2 = 8 hours. Since Mary gave John $y, we can write the equation as:

\(\frac{20+y}{10} = \frac{20-y}{8}\)

Solving this yields 18y = 40 or y = 40/18

Since the original amount we picked was 20, we need 20/(40/18) = (20/40)*18 = 18/2 = 9. Hence E.
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Originally posted by ColumbiaEMBA on 15 May 2018, 12:33.
Last edited by ColumbiaEMBA on 15 May 2018, 14:18, edited 2 times in total.
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 15 May 2018, 13:35
Walkabout 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


pushpitkc

i was wondering why my equation doesnt work if we talk about hourly wage and we know how many hours john and mary worked

\(\frac{10x+y}{10} = \frac{8x-y}{8}\)

any idea? :?
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 15 May 2018, 14:19
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dave13 wrote:
Walkabout 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


pushpitkc

i was wondering why my equation doesnt work if we talk about hourly wage and we know how many hours john and mary worked

\(\frac{10x+y}{10} = \frac{8x-y}{8}\)

any idea? :?

Look at my answer above yours. They were both paid $x. Your equation is saying that $x is the hourly rate and that John made 10*$x and Mary made 8*$x which means they made a different total amount, which is not what the problem says.
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 15 May 2018, 19:09
Walkabout 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


(x+y)/(x-y)=10/8
x=9y
E
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 22 Aug 2018, 01:49
Walkabout 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


Hi GMATPrepNow
I was trying to find an alternate solution using ratios, but got stuck up at one point. Can you help me .
Say John's Rate is R and Mary's Rate is L
then
10* R= 10R
8* L=8L
we are given that 10R= 8L
then \(\frac{R}{L}\)= \(\frac{8}{10},\)
Let \(\frac{R}{L}\)= \(\frac{8X}{10X},\)
since we are told that mary gave John y so that their rates are equal

\(\frac{8X+y}{10X-y},\)= \(\frac{1}{1}\)

we get X=y

Substituting x=y in below equation we get
\(\frac{8y+y}{10y-y},\)
\(\frac{9y}{9y},\)
that means
\(\frac{R}{L}\)= \(\frac{9y}{9y},\)
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John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 18 May 2019, 19:29
Initially they are given the same amount x and we want to equalize their rate of earnings per hour, the issue is that they work different amounts of time so this becomes a weighted average problem. Also, because they work different amounts of time the totals won't be equal after the change and plugging in becomes complicated... this was my initial confusion in setting up this problem via plugging in... that we are looking for x divided by the new rate).

1) Initial Work (wage) is x = $360
--- J works 10hr, his initial wage = $36/hr
--- M works 8hr, her initial wage = $45/hr

2) M wants to give J a total amount of $y dollars out of her $360 so that their hourly wages are equal.
--- Avg rate = \(\frac{(36*10 + 45*8)}{(10 + 8)}\) = \(\frac{720}{18}\) = 40
--- M's rate is reduced to 40... In other words M gives 5$ per hour (since she works 2 hours less she must give up 8 more to make up for the 2 extra hours) and J gains 4$ per hour.
So the total y given is 8*5 = 40

3) Solve for J's total wage in terms of y after the rate change.
--- \(\frac{360}{40}=\) 9 ... so 9*y (40) = x (360)

If I understood chetan2u correctly, we could just manipulate the time which is infinitely easier but I would never have thought to do this previously.

VeritasKarishma Please confirm, this was bugging me forever! I can see why you used rate=1 since it will divide everything nicely without making decimals...
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 18 May 2019, 19:53
energetics wrote:
Initially they are given the same amount x and we want to equalize their rate of earnings per hour, the issue is that they work different amounts of time so this becomes a weighted average problem. Also, because they work different amounts of time the totals won't be equal after the change and plugging in becomes complicated... this was my initial confusion in setting up this problem via plugging in... that we are looking for x divided by the new rate).

1) Initial Work (wage) is x = $360
--- J works 10hr, his initial wage = $36/hr
--- M works 8hr, her initial wage = $45/hr

2) M wants to give J a total amount of $y dollars out of her $360 so that their hourly wages are equal.
--- Avg rate = \(\frac{(36*10 + 45*8)}{(10 + 8)}\) = \(\frac{720}{18}\) = 40
--- M's rate is reduced to 40... In other words M gives 5$ per hour (since she works 2 hours less she must give up 8 more to make up for the 2 extra hours) and J gains 4$ per hour.
So the total y given is 8*5 = 40

3) Solve for J's total wage in terms of y after the rate change.
--- \(\frac{360}{40}=\) 9 ... so 9*y (40) = x (360)

If I understood chetan2u correctly, we could just manipulate the time which is infinitely easier but I would never have thought to do this previously.

VeritasKarishma Please confirm, this was bugging me forever! I can see why you used rate=1 since it will divide everything nicely without making decimals...



Yes, you can..
I could also simply take 360 for 10+8 or 20$ per hour.
So J should get 20*10 and M, 8*20. But each have 360/2=180, so M should give 20$.
Thus y becomes 20. Since both J and M get 180, which is 9*20 or 9y, our answer becomes 9y
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 18 May 2019, 22:45
energetics wrote:
Initially they are given the same amount x and we want to equalize their rate of earnings per hour, the issue is that they work different amounts of time so this becomes a weighted average problem. Also, because they work different amounts of time the totals won't be equal after the change and plugging in becomes complicated... this was my initial confusion in setting up this problem via plugging in... that we are looking for x divided by the new rate).

1) Initial Work (wage) is x = $360
--- J works 10hr, his initial wage = $36/hr
--- M works 8hr, her initial wage = $45/hr

2) M wants to give J a total amount of $y dollars out of her $360 so that their hourly wages are equal.
--- Avg rate = \(\frac{(36*10 + 45*8)}{(10 + 8)}\) = \(\frac{720}{18}\) = 40
--- M's rate is reduced to 40... In other words M gives 5$ per hour (since she works 2 hours less she must give up 8 more to make up for the 2 extra hours) and J gains 4$ per hour.
So the total y given is 8*5 = 40

3) Solve for J's total wage in terms of y after the rate change.
--- \(\frac{360}{40}=\) 9 ... so 9*y (40) = x (360)

If I understood chetan2u correctly, we could just manipulate the time which is infinitely easier but I would never have thought to do this previously.

VeritasKarishma Please confirm, this was bugging me forever! I can see why you used rate=1 since it will divide everything nicely without making decimals...


Yes, $1/hour, $1/item (in Profit/Loss questions) are some values I commonly assume. That way, I avoid fractions and too many different numbers.
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 25 Sep 2019, 08:42
It was an easy question once I figured out the right equation which took me a hell lot of time.
(x+y)/10=(x-y)/8
x=9y
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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New post 26 Sep 2019, 14:01
Hi All,

This question can be solved by TESTing VALUES. Here's how to do so:

In the second sentence, we're told that John worked for 10 hours and Mary worked for 8 hours... thus, 18 total hours were worked. We have to do a little more work before we pick a value for X though...

For the sake of using a nice, "round" number, let's say that the hourly pay for BOTH John and Mary should be $10/hour. This means that the entire 18-hour job should cost...

(18)($10) = $180.

The first sentence tells us that John and Mary were paid the SAME X-Dollar payment in advance though, so that $180 was split in HALF.... $90 for John and $90 for Mary.

At this point, John worked 10 hours for $90....
and Mary worked 8 hours for $90.

Mary gives John enough of her money ($Y) so that they both have the same hourly pay (the $10/hour that we chose earlier). Thus, Mary would have to give John $10. Now, the totals would be....

John worked 10 hours for $90 + $10 = $100 (re: $10/hour)
and Mary worked 8 hours for $90 - $10 = $80 (re: $10/hour)

So Y = 10 and we're looking for an answer that equals 90. That result is actually really easy to spot...

Final Answer:

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Re: John and Mary were each paid x dollars in advance to do a   [#permalink] 26 Sep 2019, 14:01

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