OG PS #204 - another way to solve??

[aznmexicana]

Is there another way to solve this problem other than what's given in the book? possibly a faster way? I tried picking numbers, but i couldnt find the right one.

John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hrs and Mary worked 2 hrs less than John. If Mary gave Jon y dollars for 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

Thanks.

[vipin85]

I do not have the OG with me right now and hence do not know their solution. I have given below my solution to this:

Both got x dollars, but John worked 10 hours and Mary worked 8 hours. This means they were each paid for 9 hours, but John worked 1 hour more than Mary.
So Mary giving John y dollars for the ONE extra hour he has put in means, their hourly wage is y. This means, John would have been paid 9y in advance (anticipating only 9 hours of work).

[rohit_gmat]

I think its best to do this by plugging in numbers.

Say x=10
So in hourly wages :
J = 10$/10hr = 1 $/hr
M = 10$/(10-2)hr = 10/8 = 5/4 $/hr
if M = (10-y)/8 which shud equal J = 10/10
we can calculate easily that y=2

So, the advance (x) in terms of y should be 10 = 5(2) = 5y
(B)

comments?

[jothi]

We can solve this problem by plugging in,

The amount paid in dollars in advance,x be 18
And Mary has given y dollars to John.Let y=2
then, (18+2)/10 = $2/hr for John
(18-2)/8= $2/hr for Mary

x=18=9x2;9xY
X=9Y

Ans : E

We can also solve this without plugging in,

(x+y)/10 = (x-y)/8
Solving, 18y=2x
x=9y

Ans : E

Is there another way to solve this problem other than what's given in the book? possibly a faster way? I tried picking numbers, but i couldnt find the right one.

John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hrs and Mary worked 2 hrs less than John. If Mary gave Jon y dollars for 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

Thanks.

[kmittal82]

Doesn't look too complicated to do by algebra either. I'm sorry I dont have the OG book, but here is my explanation

Jon's hourly wage = x/10
Mary's hourly wage = x/8

When Mary gives Jon $y, she only has $(x-y) left with her, and Jon now has $(x+y)

Thus, hourly wage for Jon = (x+y)/10 and for Mary = (x-y)/8

=> (x+y)/10 = (x-y)/8

Solve for x to get x = 9y

[GMATGuruNY]

Is there another way to solve this problem other than what's given in the book? possibly a faster way? I tried picking numbers, but i couldnt find the right one.

John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hrs and Mary worked 2 hrs less than John. If Mary gave Jon y dollars for 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

Thanks.

Whenever there are variables in the answer choices, you can plug in. Sometimes the trick is to determine the best place to plug in. Since we want John and Mary to receive the same hourly wage, let's plug in for the hourly wage.

w = $2/hr.

John works 10 hours. He should earn 10 * 2 = $20.
Mary works 8 hours. She should earn 8 * 2 = $16.
The total earned is 20 + 16 = $36.
So each was paid in advance x = $18.
For John to earn $20 and Mary to earn $16, Mary must give John y = $2.

How much was John paid in advance? With our numbers, John was paid $18.

Only answer choice E works: 9y = 9 * 2 = $18.

Hope this helps!

[rohit_gmat]

I think its best to do this by plugging in numbers.

Say x=10
So in hourly wages :
J = 10$/10hr = 1 $/hr
M = 10$/(10-2)hr = 10/8 = 5/4 $/hr
if M = (10-y)/8 which shud equal J = 10/10
we can calculate easily that y=2

So, the advance (x) in terms of y should be 10 = 5(2) = 5y
(B)

comments?

I guess this is where I went wrong -
"if M = (10-y)/8 which shud equal J = 10/10"

it should've been:
if rates are the same, then :
M rate= (10-y)/8 = (10+y)/10 = J rate
100-10y = 80 + 8y
20 = 18y
y = 10/9
x = 10, so in terms of y, x = 9y (E)