2007 AMC 10B Problem 12

Attempt Problem 12 of the 2007 AMC 10B 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 10B solutions, or check the answer key.

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12.

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

Express the children’s total age

N

years ago in terms of

T

and

N

T-N=2(T-3N)

N

years ago Tom’s age was

T-N,

and the sum of his three children’s ages was

T-3N.

The condition gives

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

T-N=2T-6N,

which simplifies to

5N=T.

Therefore

\frac{T}{N}=5.

Thus, the correct answer is D.

Problem 12 in other years