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If (c-a)/(c-b) = 2, then (5b-5a)/(c-a) =

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If (c-a)/(c-b) = 2, then (5b-5a)/(c-a) = [#permalink]

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New post 05 Nov 2017, 08:40
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If (c-a)/(c-b) = 2, then (5b-5a)/(c-a) = [#permalink]

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New post 05 Nov 2017, 09:29
Bunuel wrote:
If \(\frac{c-a}{c-b} = 2\), then \(\frac{5b-5a}{c-a} =\)

A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5

Choose values that make the equation true. Use values to solve. I used two sets. The algebra here looks time-consuming. Choosing values was quick.

\(\frac{c-a}{c-b} = 2\)

\(c = 8\)
\(a = 4\)
\(b = 6\)

Chosen values satisfy the equation:
\(\frac{8-4}{8-6}=\frac{4}{2} = 2\)

\(\frac{5b-5a}{c-a} =?\)

\(\frac{5(6)-5(4)}{8-4}=\frac{(30-20)}{4}=\frac{10}{4}= 2.5\)

Check:

\(\frac{c-a}{c-b} = 2\)

\(c = 10\)
\(a = 4\)
\(b = 7\)

\(\frac{10-4}{10-7}=\frac{6}{3} = 2\)

\(\frac{5b-5a}{c-a} =?\)

\(\frac{5(7)-5(4)}{10-4}=\frac{(35-20)}{6}=\frac{15}{6}= 2.5\)

Answer E
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Last edited by generis on 05 Nov 2017, 09:34, edited 1 time in total.
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Re: If (c-a)/(c-b) = 2, then (5b-5a)/(c-a) = [#permalink]

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Bunuel wrote:
If \(\frac{c-a}{c-b} = 2\), then \(\frac{5b-5a}{c-a} =\)

A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5


\(\frac{c-a}{c-b} = 2\)

\(c-a = 2 * c-b\)

\(c-a = 2c - 2b\)

\(2b-a = c\)

\(b + b - a = c\)

\(b-a = c-b\)

\(5 * \frac{b-a}{c-a}\)

\(5 * \frac{c-b}{c-a}\)

\(5 * \frac{1}{2}\)

\(2.5\)
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If (c-a)/(c-b) = 2, then (5b-5a)/(c-a) = [#permalink]

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New post 05 Nov 2017, 10:08
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We have been given that \(\frac{c-a}{c-b} = 2\)

Cross multiplying we get c-a = 2c-2b. Therefore c = 2b-a

Now, we need to find the value of \(\frac{5b-5a}{c-a}\)

This can be further simplified as \(\frac{5(b-a)}{c-a} = \frac{5(b-a)}{2b-2a} = \frac{5(b-a)}{2(b-a)} = 2.5\)(Option E)
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Re: If (c-a)/(c-b) = 2, then (5b-5a)/(c-a) = [#permalink]

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New post 08 Nov 2017, 16:38
Bunuel wrote:
If \(\frac{c-a}{c-b} = 2\), then \(\frac{5b-5a}{c-a} =\)

A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5


Let’s multiply both sides of the given equation by c - b:

c - a = 2c - 2b

2b - a = c

Let’s rewrite the given expression as follows:

(5b - 5a)/(c - a) = (5/2)[(2b - 2a)/(c - a)]

Note that (2b - 2a)/(c - a) = (2b - a - a)/(c - a).

Substituting c for 2b - a in the numerator, we obtain (c - a)/(c - a) = 1.

Thus, (5b - 5a)/(c - a) = (5/2)[(2b - 2a)/(c - a)] = (5/2)(1) = 2.5.

Answer: E
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Re: If (c-a)/(c-b) = 2, then (5b-5a)/(c-a) =   [#permalink] 08 Nov 2017, 16:38
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