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

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Carcass
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Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post   17 Apr 2020, 10:49
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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?

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Re: Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post   17 Apr 2020, 11:05
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Carcass wrote:
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?

Show: :: OA
100


Here's one approach:

Let J = Jennifer's $
Let B = Brian's $

Jennifer has 60 dollars more than Brian.
So, J = B + 60

If Jennifer were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have.
If Jennifer were to give Brian 1/5 of her money, then Jennifer has (4/5)J dollars, and Brian has B + (1/5)J dollars

If Brian has 25% less than the amount that Jennifer has, then Brian's amount = 3/4 Jennifer's amount.
So, we can write: (3/4)(4/5)J = B + (1/5)J
Simplify, to get (3/5)J = B + (1/5)J
Multiply both sides by 5 to get: 3J = 5B + J
Rearrange: 2J = 5B

We now have the system:
J = B + 60
2J = 5B

When we solve it, we get J = 100 (as well as B = 40)

Answer: 100

Cheers,
Brent
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nicolai123
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Re: Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post   07 Feb 2021, 10:02
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Hi, how did you get to 100 from the 2J = 5B. Thanks!We now have the system:
J = B + 60
2J = 5B

When we solve it, we get J = 100 (as well as B = 40)
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Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post   07 Feb 2021, 10:15
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nicolai123 wrote:
Hi, how did you get to 100 from the 2J = 5B. Thanks!We now have the system:
J = B + 60
2J = 5B

When we solve it, we get J = 100 (as well as B = 40)


One approach is to take J = B + 60 and rewrite it as B = J - 60 (by subtracting 60 from both sides of the equation)
Then take the other equation, 2J = 5B and replace B with J - 60 to get: 2J = 5(J - 60)
Expand: 2J = 5J - 300
Subtract 5J from both sides: -3J = -300
Divide both sides by -3 to get: J = 100

Cheers,
Brent
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Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post   08 Feb 2021, 01:11
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J = 60 + B ...... (1)

Since, J gave 1/5th of her money to B,
J = 0.8J
B = B + 0.2J

J / B = 100 / 75 = 0.8J / (B + 0.2J)
4(B + 0.2J) = 3(0.8J)
4B = 1.6J
5B = 2J ......(2)

Substitute (2) in (1);
J = 60 + 0.4J
0.6J = 60
J = 100
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Re: Jennifer has 60 dollars more than Brian. If she were to give [#permalink] New post   04 Jun 2023, 07:21
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Jennifer has 60 dollars more than Brian. If she were to give [#permalink]
04 Jun 2023, 07:21
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