2007 AMC 12B Problem 8

Attempt Problem 8 of the 2007 AMC 12B 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 2007 AMC 12B solutions, or check the answer key.

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

Tom’s age is

T

years, which is also the sum of the ages of his three children. His age

N

years ago was twice the sum of their ages then. What is

\frac{T}{N}?

2

3

4

5

6

N

years ago Tom was

T-N;

each child was

N

years younger

The children then totaled

T-3N;

set

T-N=2(T-3N)

Tom’s age

N

years ago was

T-N.

His three children were each

N

years younger, so their ages then totaled

T-3N.

The condition gives

T-N=2(T-3N),

5N=T

and

\frac{T}{N}=5.

Thus, the correct answer is D.

Problem 8 in other years