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If (m +n)/ (4 + 5) = m/4 + n/5

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If (m +n)/ (4 + 5) = m/4 + n/5 [#permalink] New post 23 May 2016, 15:22
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Question Stats:

67% (01:19) correct 32% (01:08) wrong based on 40 sessions
If \(\frac{(m +n)}{(4 + 5)} = \frac{m}{4} + \frac{n}{5}\), which of the following statements must be true?

A. m = n
B. 5m = 4n
C. 5m = –4n
D. 25m = 16n
E. 25m = –16n



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Question: 13
Page: 83
[Reveal] Spoiler: OA

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Re: If (m +n)/ (4 + 5) = m/4 + n/5 [#permalink] New post 23 May 2016, 16:03
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sandy wrote:
If \(\frac{(m +n)}{(4 + 5)} = \frac{m}{4} + \frac{n}{5}\), which of the following statements must be true?

A. m = n
B. 5m = 4n
C. 5m = –4n
D. 25m = 16n
E. 25m = –16n


We can simplify the given equation:

(m+n)/(4+5) = m/4 + n/5

(m+n)/9 = 5m/20 + 4n/20

(m+n)/9 = (5m+4n)/20

Cross multiplying gives us:

20m + 20n = 45m + 36n

-16n = 25m

Answer: E
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Re: If (m +n)/ (4 + 5) = m/4 + n/5 [#permalink] New post 12 Jun 2019, 08:57
Expert's post
sandy wrote:
If \(\frac{(m +n)}{(4 + 5)} = \frac{m}{4} + \frac{n}{5}\), which of the following statements must be true?

A. m = n
B. 5m = 4n
C. 5m = –4n
D. 25m = 16n
E. 25m = –16n



GIVEN: \(\frac{m+n}{4 + 5} = \frac{m}{4} + \frac{n}{5}\)

Simplify left side denominator: \(\frac{m+n}{9} = \frac{m}{4} + \frac{n}{5}\)

Rewrite right side with COMMON denominators: \(\frac{m+n}{9} = \frac{5m}{20} + \frac{4n}{20}\)

Simplify right: \(\frac{m+n}{9} = \frac{5m+4n}{20}\)

Cross multiply to get: \((9)(5m+4n) = (20)(m+n)\)

Expand both sides to get: \(45m+36n = 20m+20n\)
Subtract 20m from both sides to get: \(25m+36n = 20n\)
Subtract 36n from both sides to get: \(25m = -16n\)

Answer: E

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Brent
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Re: If (m +n)/ (4 + 5) = m/4 + n/5   [#permalink] 12 Jun 2019, 08:57
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