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

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2015 AMC 12A Problem 4

Below is the professionally curated solution for Problem 4 of the 2015 AMC 12A, 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 of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:ratio and proportion linear equation

Difficulty rating: 1200

4.

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

$\dfrac{5}{4}$

$\dfrac{3}{2}$

$\dfrac{9}{5}$

$2$

$\dfrac{5}{2}$

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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