What is the ratio of y to x if (x + 3y) / ( x - y) = 3/4?

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What is the ratio of y to x if $$\frac{(x+3y)}{\left(x-y\right)}=\frac{3}{4}?$$

A) -15/4
B) -5/3
C) -1/15
D) 3/5
E) 15/1

The OA is C.

Experts, additionally to the algebraic solution, is there another approach to solve this PS question? Thanks!

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by [email protected] » Mon Mar 12, 2018 10:32 am
swerve wrote:What is the ratio of y to x if $$\frac{(x+3y)}{\left(x-y\right)}=\frac{3}{4}?$$

A) -15/4
B) -5/3
C) -1/15
D) 3/5
E) 15/1

The OA is C.

Experts, additionally to the algebraic solution, is there another approach to solve this PS question? Thanks!
Well, I see '15' coming up repeatedly in the answer choices. So let's say I make x = 15. We'd have. (15 + 3y)/(15 - y) = 3/4; Now I'd just solve for y
4(15+3y) = 3(15 - y)
60 + 12y = 45 - 3y
15 = -15y
-1 = y

If x = 15 and y = -1, then y/x = -1/15. The answer is C
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by [email protected] » Sun Jun 09, 2019 5:57 pm
swerve wrote:What is the ratio of y to x if $$\frac{(x+3y)}{\left(x-y\right)}=\frac{3}{4}?$$

A) -15/4
B) -5/3
C) -1/15
D) 3/5
E) 15/1
/quote]

Cross multiplying, we have:

4x + 12y = 3x - 3y

15y = -x

y/x = -1/15

Answer: C

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