2006 AMC 12A Problem 7

Attempt Problem 7 of the 2006 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 2006 AMC 12A solutions, or check the answer key.

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Mary is $20\%$ older than Sally, and Sally is $40\%$ younger than Danielle. The sum of their ages is $23.2$ years. How old will Mary be on her next birthday?

$7$

$8$

$9$

$10$

$11$

Answer: B

Concepts:percentage linear equation

Difficulty rating: 1240

Solution:

Let Danielle be $x$ years old. Then Sally is $0.6x$ and Mary is $1.2(0.6x) = 0.72x.$

The sum $x + 0.6x + 0.72x = 2.32x = 23.2$ gives $x = 10.$ So Mary is $0.72(10) = 7.2$ years old, and on her next birthday she will be $8.$

Thus, the correct answer is B.

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