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Jennifer has 60 dollars more than Brian. If she were to give

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Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post 11 Mar 2012, 12:14
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Question Stats:

68% (01:34) correct 32% (01:16) wrong based on 25 sessions
Jennifer has 60 dollars more than Brian. If she were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have. How much money does Jennifer have?

A. 40
B. 100
C. 120
D. 140
E. 180

I got the answer wrong and the correct answer is B. I worked to get to B but I have the doubt which I highlighted below. Why it will be 75% and not 25%?

If we denote the amount of money owned by Jennifer as j and that owned by Brian as b, we can create two equations based on the information in the problem. First, Jennifer has 60 dollars more than Brian: j = b + 60.

Second, if she were to give Brian 1/5 of her money, she would have j – (1/5)j = (4/5)j dollars. Brian would then have b + (1/5)j dollars. Therefore, since Brian’s amount of money would be 75% of Jennifer’s, we can create another equation: b + (1/5)j = (0.75)(4/5)j, which can be simplified as follows:
b + (1/5)j = (0.75)(4/5)j
b + (1/5)j = (3/4)(4/5j)
b + (1/5)j = (3/5)j
b = (3/5)j – (1/5)j
b = (2/5)j

Substitute this expression for b back into the first equation, then solve for j:
j = b + 60
j = (2/5)j + 60
j – (2/5)j = 60
(3/5)j = 60
j = (60)(5/3) = 100
Therefore, Jennifer has 100 dollars.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 11 Mar 2012, 12:34, edited 1 time in total.
Edited the OA
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Re: Money with Jennifer and Brian [#permalink] New post 11 Mar 2012, 12:33
Expert's post
Jennifer has 60 dollars more than Brian. If she were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have. How much money does Jennifer have?
A. 40
B. 100
C. 120
D. 140
E. 180

Jennifer has 60 dollars more than Brian --> J=B+60;

If Jennifer were to give Brian 1/5 of her money, she would have 4/5*J and Brian would have B+1/5*J=(J-60)+1/5*J;

After that Brian would have 25% less than the amount that Jennifer would then have, so Brian would have 100%-25%=75% (3/4th) of the amount that Jennifer would then have --> 3/4*(4/5*J)=(J-60)+4/5*J --> 3J/5=6J/5-60 --> 3J=6J-300 --> J=100.

Answer: B.

Hope it's clear.

P.S. Notice that this question is a good candidate for backsolving.
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Re: Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post 11 Mar 2012, 15:17
This is how I did it. Could someone tell me if it is flawed or if you can do it this way?

J-60 = Brian's money
J(.2) = Amount given to Brian
J(.8) = Jennifer after giving away money
J(.75) = Percentage of Jennifer's money that Brian's is after she gave him .25 of her money

Brian + Money Jennifer gave to Brian = Jennifer's money after giving to brign * Percentage of Jennifer's money that Brian's money is equal to.

J-60+J(.2)=J(.8)(.75)
J-60+J(.2)=J(.6)
J-60=J(.6)-J(.2)
J-60=J(.4)
J-J(.4)=60
J(.6)=60
J=100
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Re: Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post 11 Mar 2012, 22:52
Expert's post
Stoneface wrote:
This is how I did it. Could someone tell me if it is flawed or if you can do it this way?

J-60 = Brian's money
J(.2) = Amount given to Brian
J(.8) = Jennifer after giving away money
J(.75) = Percentage of Jennifer's money that Brian's is after she gave him .25 of her money

Brian + Money Jennifer gave to Brian = Jennifer's money after giving to brign * Percentage of Jennifer's money that Brian's money is equal to.

J-60+J(.2)=J(.8)(.75)
J-60+J(.2)=J(.6)
J-60=J(.6)-J(.2)
J-60=J(.4)
J-J(.4)=60
J(.6)=60
J=100


Your approach is correct, basically it's the same as mine: you just use decimals instead of fractions.
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Re: Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post 12 Mar 2012, 06:11
assume B = x
J= x +60
1/5J = x/5 +12
J= 4/5X+48
B x+x/5+12
now 25/100*4/5x +25/100*48
x/5+12
implies 4/5x +48- x/5-12
implies 6/5x+12= 3/5X36
implies X = 40
we are looking for jenifer its x +60 so jenifier is 100
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Re: Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post 12 Mar 2012, 06:45
My Way of doing it :-

Brian= x
Jenifer= 60+x
When jenifer gave one fifth of her money to brian ,then money with brian will be equal to 75% of the money that is remaining with Jenifer. So we can make the following equation :

x+1/5(60+x)= 75%[60+x-1/5(60+x)
Solve it and you will get:

x= 40
and amount with jenifer will be = 60+x
= 60+40= 100

I hope the simple explanation helps.
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Re: Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post 12 Mar 2012, 07:02
If B = x
J = B + 60 = x + 60 ----(1)

(75%)(4/5)(J) = B + (1/5)(J)

We get (2/5)*J = B ----(2)

Substitute (2) in (1)

J = 100; B = 40

I hope I am clear with the solution
Re: Jennifer has 60 dollars more than Brian. If she were to give   [#permalink] 12 Mar 2012, 07:02
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