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ps 500 test27 #16

This topic has 3 expert replies and 2 member replies

ps 500 test27 #16

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16. 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,
the answer is E) but could not set an equation to it... can anyone please explain?

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dunkin77 wrote:
16. 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,
the answer is E) but could not set an equation to it... can anyone please explain?
... since mary is giving away y dollars form her payement to john her payement becomes x - y ... and since john receives this payement of y dollars his poayement becomes x + y ... now it is given that after this transaction their both hourly wage shuld be the same .. that is (x + y)/10 = (x - y)/8 .. cross multiplying we get 8x + 8y = 10x - 10y ... which is 2x = 18y .. therfore x = 9y .. and hence the answer

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Wages same so D1/D2=H1/H2

(X+Y)/(X-Y) = 10/8

(X+Y)/(X-Y) =5/4 ==> X=9Y

Note: Trick in general is just to take ratios when a variable is same.

Speed=distance/time ==> S -> 1/t when distance is same etc..

R

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dunkin77 wrote:
16. 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. It follows that:

John’s hours = 10

Mary’s hours = 8

We are also given that John and Mary were each given x dollars in advance. We are also told that Mary gave John y dollars of her payment so that they would have an equal hourly wage. It follows that Mary actually made x - y dollars. Since John received y dollars, he now made x + y dollars. Using this information, the hourly wages of John and Mary are:

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

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 solve:

8x + 8y = 10x - 10y

-2x = -18y

x = 9y

Answer: E

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dunkin77 wrote:
16. 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
One approach:

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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dunkin77 wrote:
16. 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
John and Mary were each paid x dollars in advance to do a certain job together.
John worked on the job for 10 hours.
Mary worked 2 hours less than John.

Since a total of 18 hours are worked -- 10 hours by John, 8 hours by Mary -- let x=18.
Since John and Mary are each given $18 in advance, the total pay for the job = 18+18 = 36.
Since Mary works 8 of the 18 hours, she takes home 8/18 of the total pay:
(8/18)(36) = 16.

Mary gave John y dollars of her payment.
Since Mary was given $18 in advance but takes home only $16, she gave John $2, implying that y=2.

What was the dollar amount that John was paid in advance?
Since John was given $18 in advance, the correct answer must yield $18 when y=2.
Only E works:
9y = 9*2 = 18.

The correct answer is E.

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