2017 AMC 10B Problem 4

Problem 4 of 25EasierAlgebra

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}?

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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 .

Concepts: rational equation · algebraic manipulation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.