2017 AMC 10B Problem 4 — Solution | LIVE by Po-Shen Loh

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2017 AMC 10B Problem 4

Attempt Problem 4 of the 2017 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2017 AMC 10B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

4.

Suppose that $x$ and $y$ are nonzero real numbers such that $\frac{3x+y}{x-3y}=-2.$ What is the value of $\frac{x+3y}{3x-y}?$

$-3$

$-1$

$1$

$2$

$3$

Answer: D

Concepts:rational equation algebraic manipulation

Difficulty rating: 900

Solution:

Given that $\frac{3x+y}{x-3y}=-2,$ we can multiply by the denominator to get $3x+y = 6y-2x.$ Solving, we can see that $x=y.$

Therefore, $\frac{x+3y}{3x-y} = \frac{x+3x}{3x-x}=2.$

Thus, the correct answer is D .

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