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Could someone also do this problem plugging numbers. I tried but it is not working.
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runningguy wrote:
Could someone also do this problem plugging numbers. I tried but it is not working.


I had trouble coming up with the above approach so i tried plugging numbers.

You are told John worked 10 hrs and Mary worked 8, and they are EACH paid x dollars for their work. I chose 80 for x since it's a multiple of
8 and 10. In this case, John is paid 8/hr and Mary is paid 10/hr. Since they have to be paid the same amount, Mary gives $1 to John (remember, y represents the amount of money she gives to John, so here y = 1). John now earns $9/hr or 9y.
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Re: John and Mary were each paid x dollars in advance to do a [#permalink]
I tried this but I am not getting the answer.

Lets assume Both John and Mary got 8 and 8 advance.
Mary gave john $2 as she worked 2 hour less.
So y=2.
Answer: a.

Where am I going wrong?
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theGame001 wrote:
I tried this but I am not getting the answer.

Lets assume Both John and Mary got 8 and 8 advance.
Mary gave john $2 as she worked 2 hour less.
So y=2.
Answer: a.

Where am I going wrong?


We are told that after Mary gave John y dollars they received the same hourly wage. Your example does not provide that. Try using $9 advance pay instead or check Karishma's post for number plugging here: john-and-mary-were-each-paid-x-dollars-in-advance-to-do-a-144782.html#p1294268 or algebraic approach here: john-and-mary-were-each-paid-x-dollars-in-advance-to-do-a-144782.html#p1161559

Hope this helps.
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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 worked 10 hours and paid x dollars
Mary worked 8 hours and paid x dollars

John and Mary together worked: \(10 + 8 = 18 hours\)
John and Mary together paid :\(x + x = 2x\)

Hence, hourly wage or wage/hour \(= 2x/18\) or \(x/9\)

As per hourly wage, john is paid less by an amount \((x/9)*10 - x\) Or, \(x/9\)
Or, Mary is paid more by an amount \(x - (x/9)*10\) or \(x/9\)

Or, \(x/9\) is the amount Mary gave John so that they would have received the same hourly wage.
Or, \(x/9 = y\)
Or, \(x = 9y\)

Hence, answer (E)
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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


Let us say that both got $ 40 for the job, x = 40

John --- 10 hours ---- $ 40 ----- After paying ---- 40 + y
Mary --- 8 hours ------ $ 40 ----- After paying ----- 40 - y

Now the rate is same: (40 + y)/10 = (40 - y)/8
160 + 4y = 200 - 5y
9y = 40
y = 40/9

By putting y = 40/9 we should get x = 40 which is answer option E.
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VeritasPrepKarishma wrote:
runningguy wrote:
Could someone also do this problem plugging numbers. I tried but it is not working.


Number plugging could work like this:

John worked on the job for 10 hours and Mary worked for 8 hours. They were both paid an equal amount but Mary gave John some of her amount so that they both get the same hourly wage. We can easily imagine this by assuming that they both got $9 each initially and Mary gave $1 to John so that Mary got $8 (@$1 per hr) and John got $10 (@ $1 per hr).
So x could be $9
and y could be $1.
We need x in terms of y which is x = 9y


Hi Karishma,

I actually tried the number approach as well and did EXACTLY that, with those same exact numbers, but for some reason, didn't think that the answer was the right answer.

Mary worked 8 hours.
John worked 10 hours.

Let's say they both earned 80 dollars, which would make:

Mary's hourly wage: $10/hr
John's hourly wage: $8/hr

To get the same wage, lets say 9, mary would earn $9/hr and John would earn $11/hr. But doing so, the total gets misaligned. Now, Mary's total wage will be (9$/hr)(8hr) = $72 and John's will be (11$/hr)(10hr) = $110. Don't they need to earn the same TOTAL money? How can this work if they need to earn the same total?

Thanks!

Bunuel 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


The amount Mary has in the end is x-y dollars and she worked for 8 hours;
The amount John has in the end is x+y dollars and he worked for 10 hours;;

We are told that in this case their hourly wage was the same: \(hourly \ wage=\frac{wage}{# \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10}\), from \(\frac{x-y}{8}=\frac{x+y}{10}\) we get that \(x=9y\).

Answer: E.


Bunuel,

I can completely follow the logic below but I had no idea that we were solving for x. How did you come up with the concept, albeit correct, that we were solving for x?

Thanks!
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russ9 wrote:
VeritasPrepKarishma wrote:
runningguy wrote:
Could someone also do this problem plugging numbers. I tried but it is not working.


Number plugging could work like this:

John worked on the job for 10 hours and Mary worked for 8 hours. They were both paid an equal amount but Mary gave John some of her amount so that they both get the same hourly wage. We can easily imagine this by assuming that they both got $9 each initially and Mary gave $1 to John so that Mary got $8 (@$1 per hr) and John got $10 (@ $1 per hr).
So x could be $9
and y could be $1.
We need x in terms of y which is x = 9y


Hi Karishma,

I actually tried the number approach as well and did EXACTLY that, with those same exact numbers, but for some reason, didn't think that the answer was the right answer.

Mary worked 8 hours.
John worked 10 hours.

Let's say they both earned 80 dollars, which would make:

Mary's hourly wage: $10/hr
John's hourly wage: $8/hr

To get the same wage, lets say 9, mary would earn $9/hr and John would earn $11/hr. But doing so, the total gets misaligned. Now, Mary's total wage will be (9$/hr)(8hr) = $72 and John's will be (11$/hr)(10hr) = $110. Don't they need to earn the same TOTAL money? How can this work if they need to earn the same total?

Thanks!

Bunuel 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


The amount Mary has in the end is x-y dollars and she worked for 8 hours;
The amount John has in the end is x+y dollars and he worked for 10 hours;;

We are told that in this case their hourly wage was the same: \(hourly \ wage=\frac{wage}{# \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10}\), from \(\frac{x-y}{8}=\frac{x+y}{10}\) we get that \(x=9y\).

Answer: E.


Bunuel,

I can completely follow the logic below but I had no idea that we were solving for x. How did you come up with the concept, albeit correct, that we were solving for x?

Thanks!


We are told that John was paid x dollars in advance.
The question asks: what was the dollar amount, in terms of y, that John was paid in advance? So, it asks to find x (the dollar amount that John was paid in advance) in terms of y.

Hope it's clear.
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russ9 wrote:
VeritasPrepKarishma wrote:
runningguy wrote:
Could someone also do this problem plugging numbers. I tried but it is not working.


Number plugging could work like this:

John worked on the job for 10 hours and Mary worked for 8 hours. They were both paid an equal amount but Mary gave John some of her amount so that they both get the same hourly wage. We can easily imagine this by assuming that they both got $9 each initially and Mary gave $1 to John so that Mary got $8 (@$1 per hr) and John got $10 (@ $1 per hr).
So x could be $9
and y could be $1.
We need x in terms of y which is x = 9y


Hi Karishma,

I actually tried the number approach as well and did EXACTLY that, with those same exact numbers, but for some reason, didn't think that the answer was the right answer.

Mary worked 8 hours.
John worked 10 hours.

Let's say they both earned 80 dollars, which would make:

Mary's hourly wage: $10/hr
John's hourly wage: $8/hr

To get the same wage, lets say 9, mary would earn $9/hr and John would earn $11/hr. But doing so, the total gets misaligned. Now, Mary's total wage will be (9$/hr)(8hr) = $72 and John's will be (11$/hr)(10hr) = $110. Don't they need to earn the same TOTAL money? How can this work if they need to earn the same total?

Thanks!


The numbers I have assumed are that Mary and John got a TOTAL of $9 each initially (same total wage received). Then Mary gave John $1 so that Mary got a total of $8 and John got a total of $10. They hourly wages are $1/hour (same for both). This gives x = $9 and y = $1.
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Bunuel 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


The amount Mary has in the end is x-y dollars and she worked for 8 hours;
The amount John has in the end is x+y dollars and he worked for 10 hours;;

We are told that in this case their hourly wage was the same: \(hourly \ wage=\frac{wage}{# \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10}\), from \(\frac{x-y}{8}=\frac{x+y}{10}\) we get that \(x=9y\).

Answer: E.


Hi Bunuel,

Could you please let me know where I went wrong in my approach?

I assumed that that the advance amount given to each person was 40 $. (X=40).

As John worked 10 hours and Mary worked 8 hours,

John's hourly rate = 40/10=4$/hr
Mary's houry rate = 40/8=5/hr

For Mary to receive the same hourly rate as John (4$/hr), she would have had to earn only 4*8 = 32$

Hence the amount to be given to John = 40-32=8 (i.e y = 8 in this case)

In this case 40=5(8) i.e. x=5y (option B)
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deliverance wrote:
Bunuel 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


The amount Mary has in the end is x-y dollars and she worked for 8 hours;
The amount John has in the end is x+y dollars and he worked for 10 hours;;

We are told that in this case their hourly wage was the same: \(hourly \ wage=\frac{wage}{# \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10}\), from \(\frac{x-y}{8}=\frac{x+y}{10}\) we get that \(x=9y\).

Answer: E.


Hi Bunuel,

Could you please let me know where I went wrong in my approach?

I assumed that that the advance amount given to each person was 40 $. (X=40).

As John worked 10 hours and Mary worked 8 hours,

John's hourly rate = 40/10=4$/hr
Mary's houry rate = 40/8=5/hr

For Mary to receive the same hourly rate as John (4$/hr), she would have had to earn only 4*8 = 32$

Hence the amount to be given to John = 40-32=8 (i.e y = 8 in this case)

In this case 40=5(8) i.e. x=5y (option B)


The point is that when Mary gives John y dollars of her payment, Mary's hourly wage will decrease and John's hourly wage will increase. In your case Mary's hourly wage is $4 while John's hourly wage becomes 48/10=$4.8. As you can see the hourly wages are not equal.
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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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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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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,
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John and Mary were each paid x dollars in advance to do a [#permalink]
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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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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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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