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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]  23 May 2016, 15:22
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Question Stats:

62% (01:07) correct 37% (00:50) wrong based on 27 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

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

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Re: If (m +n)/ (4 + 5) = m/4 + n/5 [#permalink]  23 May 2016, 16:03
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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

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

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Re: If (m +n)/ (4 + 5) = m/4 + n/5 [#permalink]  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: $$25m = -16n$$

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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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