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

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Manager
Joined: 29 Aug 2007
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John and Mary were each paid X dollars in advance to do a [#permalink]  14 Sep 2007, 03:45
John and Mary were each paid X dollars in advance to do a certain job together. John worked in the job for 10 Hours and Mary worked for 2 Hours less than john. If May gayve john y dollars of her payement so that they would have recieved the same hourly wage, what was the amount in terms of Y that john ws paid in advance

John has = X
Mary has = X

John worked 10 Hours = His hourly pay is 10w
Mary worked 8 hours = her hourly pay is 8w

Put for the Hourly wage to be equay mary had to give = Y dollars

so equation for Mary now for money she has is

X + 10w-y

Money that John has is X + y + 8w

How do you solve after this ! according to OG, they are equating

X -y = 8w
X+y = 10W

I dont understand how they are equating this?
VP
Joined: 08 Jun 2005
Posts: 1147
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John and Mary got paid ---> x+x = 2x

They worked for ---> 10+8 = 18 hours

so, the same amount per hour is ---> 2x/18 = x/9

Since Mary gave John y dollars of her money then:

(x-y)/8 = x/9

or

(x+y)/10 = x/9

solving for y will yield:

x-y = (x*8)/9

y = x/9

9y = x

John got in advance x dollars so ---> 9y

Manager
Joined: 29 Aug 2007
Posts: 110
Followers: 1

Kudos [?]: 2 [0], given: 0

(x-y)/8 = x/9

or

(x+y)/10 = x/9

solving for y will yield:

x-y = (x*8)/9

y = x/9

9y = x

John got in advance x dollars so ---> 9y
Quote:

How are you equating

x-y/8 = x/9?

You are equating money she has ( X -y) / the number of hours she worked to hourly wage?

VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 128 [1] , given: 0

1
KUDOS
beatgmat wrote:
(x-y)/8 = x/9

or

(x+y)/10 = x/9

solving for y will yield:

x-y = (x*8)/9

y = x/9

9y = x

John got in advance x dollars so ---> 9y
Quote:

How are you equating

x-y/8 = x/9?

You are equating money she has ( X -y) / the number of hours she worked to hourly wage?

Lets assume Mary got 180 dollars and John got 180 dollars.

they worked for a total of 18 houres.

so the average pay per hour of both of them is 360/18 = 20

since Mary got 180/8 = 22.5 per hour and John got 180/10 = 18 per hour Mary gave John (2.5*8) dollars, this is y !!! she now has 180 (i.e x) - 20 (i.e y) = 160/8 = 20 per hour.

John got y (i.e 2.5*8) dollars and now he has 180 (i.e x) + 20 (i.e y) = 200/10 = 20 per hour

9y = x

20*9 = 180

CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
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Re: [#permalink]  30 Jan 2008, 05:30
KillerSquirrel wrote:
beatgmat wrote:
(x-y)/8 = x/9

or

(x+y)/10 = x/9

solving for y will yield:

x-y = (x*8)/9

y = x/9

9y = x

John got in advance x dollars so ---> 9y
Quote:

How are you equating

x-y/8 = x/9?

You are equating money she has ( X -y) / the number of hours she worked to hourly wage?

Lets assume Mary got 180 dollars and John got 180 dollars.

they worked for a total of 18 houres.

so the average pay per hour of both of them is 360/18 = 20

since Mary got 180/8 = 22.5 per hour and John got 180/10 = 18 per hour Mary gave John (2.5*8) dollars, this is y !!! she now has 180 (i.e x) - 20 (i.e y) = 160/8 = 20 per hour.

John got y (i.e 2.5*8) dollars and now he has 180 (i.e x) + 20 (i.e y) = 200/10 = 20 per hour

9y = x

20*9 = 180

its much easier to plug in smart numbers.
$80 each person j =$8 an hour
m = $10 In order for j and m to have the same amount of money per hour, 10+8 / 2 =$9 per hour for both ppl.

m must give 1 dollar. y=1

therefore, john receives $9 dollars an hour, as does M.$9/hr in terms of y is 9y.
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Re:   [#permalink] 30 Jan 2008, 05:30
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