2015 AMC 12A Problem 4 — Solution | LIVE by Po-Shen Loh

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2015 AMC 12A Problem 4

Attempt Problem 4 of the 2015 AMC 12A 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 2015 AMC 12A solutions, or check the answer key.

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

4.

The sum of two positive numbers is $5$ times their difference. What is the ratio of the larger number to the smaller number?

$\dfrac{5}{4}$

$\dfrac{3}{2}$

$\dfrac{9}{5}$

$2$

$\dfrac{5}{2}$

Answer: B

Concepts:ratio and proportion linear equation

Difficulty rating: 1200

Solution:

Let $x$ and $y$ be the numbers with $x \gt y \gt 0.$ Then $x+y = 5(x-y).$

Expanding gives $x+y = 5x-5y,$ so $6y = 4x$ and $\dfrac{x}{y} = \dfrac{3}{2}.$

Thus, the correct answer is B.

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