2007 AMC 12B Problem 8

Below is the professionally curated solution for Problem 8 of the 2007 AMC 12B, 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.

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Concepts:ages linear equation

Difficulty rating: 1290

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 $T/N?$

$2$

$3$

$4$

$5$

$6$

Solution:

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 $T-N=2(T-3N),$ so $5N=T$ and $T/N=5.$

Thus, the correct answer is D.

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