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2006 AMC 12A Problem 7

Problem 7 of 25EasierAlgebra

Mary is 20%20\% older than Sally, and Sally is 40%40\% younger than Danielle. The sum of their ages is 23.223.2 years. How old will Mary be on her next birthday?

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Solution

Let Danielle be xx years old. Then Sally is 0.6x0.6x and Mary is 1.2(0.6x)=0.72x.1.2(0.6x) = 0.72x. The sum x+0.6x+0.72x=2.32x=23.2x + 0.6x + 0.72x = 2.32x = 23.2 gives x=10.x = 10. So Mary is 0.72(10)=7.20.72(10) = 7.2 years old, and on her next birthday she will be 8.8. Thus, the correct answer is B.

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Concepts: percentage · linear equation

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