2017 AMC 12B Problem 3

Problem 3 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

The equation gives

3x + y = -2(x - 3y)

= -2x + 6y,

5x = 5y,

meaning

x = y.

Then

\frac{x + 3y}{3x - y} = \frac{y + 3y}{3y - y} = \frac{4y}{2y} = 2.

Thus, the correct answer is D.

Concepts: algebraic manipulation · substitution

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