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

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Joined: 02 Sep 2009
Posts: 50619
If (c-a)/(c-b) = 2, then (5b-5a)/(c-a) =  [#permalink]

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05 Nov 2017, 08:40
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Difficulty:

25% (medium)

Question Stats:

85% (01:53) correct 15% (02:40) wrong based on 92 sessions

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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

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

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Updated on: 05 Nov 2017, 09:34
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:

$$\frac{c-a}{c-b} = 2$$

$$c = 10$$
$$a = 4$$
$$b = 7$$

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

$$\frac{5b-5a}{c-a} =?$$

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

Originally posted by generis on 05 Nov 2017, 09:29.
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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05 Nov 2017, 09:32
1
2
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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05 Nov 2017, 10:08
1
1
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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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.

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