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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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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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 strivingFor800 on 15 May 2018, 12:33.
Last edited by strivingFor800 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
1
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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Re: John and Mary were each paid x dollars in advance to do a &nbs [#permalink] 22 Aug 2018, 01:49

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