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Marisa has $40 more than Ben, and Ben has one-third as much
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14 Jun 2018, 14:28
14 Jun 2018, 14:28
Expert Reply
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Question Stats:
100% (00:37) correct
0% (00:00) wrong based on 33 sessions
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Marisa has $40 more than Ben, and Ben has one-third as much money as Marisa. How many dollars does Ben have?
Show: :: OA
20
Re: Marisa has $40 more than Ben, and Ben has one-third as much
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19 Jun 2018, 16:21
19 Jun 2018, 16:21
1
\(M = 40 + B\)
\(B = \frac{1}{3}M\)
\(M = 40 + \frac{1}{3}M\)
\(\frac{2}{3}M = 40\)
\(2M = 120\)
\(M = 60\)
Now that we know Marisa has 60 dollars, we plug it into the original equation.
\(60 = 40 + B\)
\(20 = B\)
Ben has 20 dollars.
\(B = \frac{1}{3}M\)
\(M = 40 + \frac{1}{3}M\)
\(\frac{2}{3}M = 40\)
\(2M = 120\)
\(M = 60\)
Now that we know Marisa has 60 dollars, we plug it into the original equation.
\(60 = 40 + B\)
\(20 = B\)
Ben has 20 dollars.
Re: Marisa has $40 more than Ben, and Ben has one-third as much
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05 Jul 2018, 01:36
05 Jul 2018, 01:36
Expert Reply
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.
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.
