2007 AMC 12B Problems/Problem 8

From AoPSWiki

Problem

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 $T/N$ ?

$\mathrm {(A)} 2$ $\mathrm {(B)} 3$ $\mathrm {(C)} 4$ $\mathrm {(D)} 5$ $\mathrm {(E)} 6$

Solution

$T=a+b+c$

$T-N=2(a-N+b-N+c-N)=2(a+b+c)-6N=2T-6N$

$2T-6N=T-N$

$T=5N$

$T/N=5 \Rightarrow \mathrm {(D)}$

2007 AMC 12B (Problems • Resources)
Preceded by Problem 7	Followed by Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

Personal tools

Navigation

Search

Toolbox

2007 AMC 12B Problems/Problem 8

From AoPSWiki

Problem

Solution

See Also