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Marisa has $40 more than Ben, and Ben has one-third as much

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1613 [0], given: 375

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Marisa has $40 more than Ben, and Ben has one-third as much [#permalink] New post 14 Jun 2018, 14:28
Expert's post
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Question Stats:

99% (00:41) correct 0% (00:00) wrong based on 7 sessions
Marisa has $40 more than Ben, and Ben has one-third as much money as Marisa. How many dollars does Ben have?

[Reveal] Spoiler: OA
20

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Sandy
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Intern
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Joined: 02 May 2018
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Kudos [?]: 25 [1] , given: 15

Re: Marisa has $40 more than Ben, and Ben has one-third as much [#permalink] New post 19 Jun 2018, 16:21
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\(M = 40 + B\)
\(B = \frac{1}{3}M\)

\(M = 40 + \frac{1}{3}M\)
\(\frac{2}{3}M = 40\)
\(2M = 120\)
\(M = 60\)

Now that we know Marisa has 60 dollars, we plug it into the original equation.

\(60 = 40 + B\)
\(20 = B\)

Ben has 20 dollars.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1613 [0], given: 375

CAT Tests
Re: Marisa has $40 more than Ben, and Ben has one-third as much [#permalink] New post 05 Jul 2018, 01:36
Expert's post
Explanation

Translate the given information. Let M equal Marisa’s money and B equal Ben’s:

\(M = B + 40\)

\(B =\frac{1}{3} M\)

The question asks for B, so solve the second equation for M and substitute into the first equation:

\(3B = M\)

\(3B = B + 40\)

\(2B = 40\)

\(B = 20\)

Check the answer. If Ben has $20 and Marisa has $40 more than Ben, she has $60. It is true that Ben has one-third as much money as Marisa.
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Sandy
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Intern
Intern
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Joined: 04 May 2017
Posts: 36
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Kudos [?]: 21 [0], given: 6

Re: Marisa has $40 more than Ben, and Ben has one-third as much [#permalink] New post 10 Jul 2018, 03:03
We have system of equations as follows: M = B + 40 and B = 1/3*M <-> M = B + 40 and M = 3B -> 3B = B + 40 -> 2B = 40 -> B = 20.
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Re: Marisa has $40 more than Ben, and Ben has one-third as much   [#permalink] 10 Jul 2018, 03:03
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