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# Marisa paid two painters, Rich and Jim, each x dollars to paint her ho

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Math Expert
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Posts: 54696
Marisa paid two painters, Rich and Jim, each x dollars to paint her ho  [#permalink]

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25 Jul 2017, 22:35
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Difficulty:

65% (hard)

Question Stats:

52% (02:24) correct 48% (02:44) wrong based on 83 sessions

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Marisa paid two painters, Rich and Jim, each x dollars to paint her house. Rich and Jim worked together for 14 hours, after which Jim took 2 more hours to finish the job. If Rich then gave Jim y dollars so that the two painters would each receive the same hourly wage, then how much was Marisa's total payment to the painters, in terms of y?

A. 2y
B. 12y
C. 15y
D. 24y
E. 30y

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Marisa paid two painters, Rich and Jim, each x dollars to paint her ho  [#permalink]

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26 Jul 2017, 01:16
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Assume the amount that was paid to both Rich and Jim be 100$(x) Once Rich gives y dollars to Jim, they receive the same hourly wage. Since their hourly rates are the same, $$\frac{100 - y}{14} = \frac{100 + y}{16}$$ Cross multiplying, we get 1600 - 16y = 1400 + 14y Here, 30y = 200 -> y = $$\frac{20}{3}$$ Total amount paid to both the painters is 200$(2*100$) On substituting the value y = $$\frac{20}{3}$$, 30y (Option E) will give us the 200$ paid to the painters.
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Re: Marisa paid two painters, Rich and Jim, each x dollars to paint her ho  [#permalink]

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26 Jul 2017, 05:38
1
Bunuel wrote:
Marisa paid two painters, Rich and Jim, each x dollars to paint her house. Rich and Jim worked together for 14 hours, after which Jim took 2 more hours to finish the job. If Rich then gave Jim y dollars so that the two painters would each receive the same hourly wage, then how much was Marisa's total payment to the painters, in terms of y?

A. 2y
B. 12y
C. 15y
D. 24y
E. 30y

Payment/Work Done
Rich = x/14 hrs
Jim = x+y/16 hrs
Same hourly wage
y is paid for 2 hrs
Total work done is 14+16 = 30 hrs
Total payment in terms of y = 15y

Please correct me if i am wrong
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Marisa paid two painters, Rich and Jim, each x dollars to paint her ho  [#permalink]

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26 Jul 2017, 06:41
1
2
mynamegoeson wrote:
Bunuel wrote:
Marisa paid two painters, Rich and Jim, each x dollars to paint her house. Rich and Jim worked together for 14 hours, after which Jim took 2 more hours to finish the job. If Rich then gave Jim y dollars so that the two painters would each receive the same hourly wage, then how much was Marisa's total payment to the painters, in terms of y?

A. 2y
B. 12y
C. 15y
D. 24y
E. 30y

Payment/Work Done
Rich = x/14 hrs
Jim = x+y/16 hrs
Same hourly wage
y is paid for 2 hrs
Total work done is 14+16 = 30 hrs
Total payment in terms of y = 15y

Please correct me if i am wrong

Your assumption that since Jim is being paid y for 2 extra hours makes the hourly wage = y/2 is incorrect.

After giving y dollars to Jim,
Rich's wage(who worked for 14 hours) = x-y
Jim's wage(who worked for 16 hours) = x+y
Difference in terms of hours= 16-14=2
Difference in terms of wage = (x+y) - (x-y) = 2y
So, 2 hours of work corresponds to a wage of '2y'(and not 'y').
And since total work is 30 Hours, total wage paid is 30y

Hope this helps.
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Re: Marisa paid two painters, Rich and Jim, each x dollars to paint her ho  [#permalink]

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26 Jul 2017, 06:45
nitesh181989 wrote:
mynamegoeson wrote:
Bunuel wrote:
Marisa paid two painters, Rich and Jim, each x dollars to paint her house. Rich and Jim worked together for 14 hours, after which Jim took 2 more hours to finish the job. If Rich then gave Jim y dollars so that the two painters would each receive the same hourly wage, then how much was Marisa's total payment to the painters, in terms of y?

A. 2y
B. 12y
C. 15y
D. 24y
E. 30y

Payment/Work Done
Rich = x/14 hrs
Jim = x+y/16 hrs
Same hourly wage
y is paid for 2 hrs
Total work done is 14+16 = 30 hrs
Total payment in terms of y = 15y

Please correct me if i am wrong

Your assumption that since Jim is being paid y for 2 extra hours makes the hourly wage = y/2 is incorrect.

After giving y dollars to Jim,
Rich's wage(who worked for 14 hours) = x-y
Jim's wage(who worked for 16 hours) = x+y
Difference in terms of hours= 16-14=2
Difference in terms of wage = (x+y) - (x-y) = 2y
So, 2 hours of work corresponds to a wage of '2y'(and not 'y').
And since total work is 30 Hours, total wage paid is 30y

Hope this helps.

Yes got it rich paid y dollars from his pocket to Jim
New amount with rich would be (x-y)
And with him would be (x+y)
And hence two hours would be equivalent to the difference that is 2y

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Re: Marisa paid two painters, Rich and Jim, each x dollars to paint her ho  [#permalink]

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26 Jul 2017, 16:19
3
Bunuel wrote:
Marisa paid two painters, Rich and Jim, each x dollars to paint her house. Rich and Jim worked together for 14 hours, after which Jim took 2 more hours to finish the job. If Rich then gave Jim y dollars so that the two painters would each receive the same hourly wage, then how much was Marisa's total payment to the painters, in terms of y?

A. 2y
B. 12y
C. 15y
D. 24y
E. 30y

Since hourly wage is payment/hours:

Rich’s hourly wage is x/14

Jim’s hourly wage is x/16

Since Rich then gave Jim y dollars so that the two painters would each receive the same hourly wage:

(x - y)/14 = (x + y)/16

16(x - y) = 14(x + y)

16x - 16y = 14x + 14y

2x = 30y

x = 15y

Since each person gets x, or 15y dollars, the pair gets a total of 30y dollars.

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Re: Marisa paid two painters, Rich and Jim, each x dollars to paint her ho  [#permalink]

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26 Jul 2017, 21:43
Bunuel wrote:
Marisa paid two painters, Rich and Jim, each x dollars to paint her house. Rich and Jim worked together for 14 hours, after which Jim took 2 more hours to finish the job. If Rich then gave Jim y dollars so that the two painters would each receive the same hourly wage, then how much was Marisa's total payment to the painters, in terms of y?

A. 2y
B. 12y
C. 15y
D. 24y
E. 30y

Bunuel,

this question got me confused.
the question says "Rich and Jim worked together for 14 hours", it is like R+J=14
I thought they work 7+7=14
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Re: Marisa paid two painters, Rich and Jim, each x dollars to paint her ho  [#permalink]

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26 Jul 2017, 22:36
pclawong wrote:
Bunuel wrote:
Marisa paid two painters, Rich and Jim, each x dollars to paint her house. Rich and Jim worked together for 14 hours, after which Jim took 2 more hours to finish the job. If Rich then gave Jim y dollars so that the two painters would each receive the same hourly wage, then how much was Marisa's total payment to the painters, in terms of y?

A. 2y
B. 12y
C. 15y
D. 24y
E. 30y

Bunuel,

this question got me confused.
the question says "Rich and Jim worked together for 14 hours", it is like R+J=14
I thought they work 7+7=14

Hi,

When they say Rich and Jim together worked for 14 hours, it doesn't mean that R+J = 14
It means R, J both work for 14 hours trying to complete the work.
And the second part of the question says J works another 2 hours.

So the equation would read R + J = 30

Hope that helps
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Re: Marisa paid two painters, Rich and Jim, each x dollars to paint her ho  [#permalink]

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26 Jul 2017, 23:41
Bunuel wrote:
Marisa paid two painters, Rich and Jim, each x dollars to paint her house. Rich and Jim worked together for 14 hours, after which Jim took 2 more hours to finish the job. If Rich then gave Jim y dollars so that the two painters would each receive the same hourly wage, then how much was Marisa's total payment to the painters, in terms of y?

A. 2y
B. 12y
C. 15y
D. 24y
E. 30y

This is very similar to the problems on votes in the election.

Marissa paid $$x$$ each to Rich and Jim = $$x + x = 2x$$.

Rich worked for 14h, while Jim worked for 16h. No. of hours worked is different but the hourly wage is the same. To adjust for this, Rich gave $$y$$ to Jim, so that they have the same hourly wage.

Rich's hourly wage = $$\frac{x-y}{14}$$

Jim's hourly wage = $$\frac{x+y}{16}$$

$$\frac{x-y}{14} = \frac{x+y}{16}$$

$$16x - 16y = 14x + 14y$$

$$2x = 30y$$. Ans - E.
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Re: Marisa paid two painters, Rich and Jim, each x dollars to paint her ho  [#permalink]

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27 Jul 2017, 05:44
Since Marisa paid Rich and Jim x dollars each ,the equation boils down to :

(x-y)/14 = (x+y)/16

16x-16 y= 14x +14 y

Solving gives x= 15 y

Therefore , the total amount given by Marissa is 15y*2= 30y.
Re: Marisa paid two painters, Rich and Jim, each x dollars to paint her ho   [#permalink] 27 Jul 2017, 05:44
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