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.

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

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

Let Danielle’s age be

x,

then express Sally’s and Mary’s ages in terms of

x

Sally

= 0.6x

and Mary

= 1.2(0.6x) = 0.72x;

the ages sum to

23.2

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.

Problem 7 in other years