Difference between revisions of "2010 AMC 8 Problems/Problem 11"
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<math> \textbf{(A)}\ 48 \qquad\textbf{(B)}\ 64 \qquad\textbf{(C)}\ 80 \qquad\textbf{(D)}\ 96\qquad\textbf{(E)}\ 112 </math> | <math> \textbf{(A)}\ 48 \qquad\textbf{(B)}\ 64 \qquad\textbf{(C)}\ 80 \qquad\textbf{(D)}\ 96\qquad\textbf{(E)}\ 112 </math> | ||
== Solution == | == Solution == | ||
| − | Let the height of the taller tree be <math>h</math> and let the height of the smaller tree be <math>h-16</math>. Since the ratio of the smaller tree to the larger tree is <math>\frac{3}{4}</math>, we have <math>\frac{h-16}{h}=\frac{3}{4}</math>. Solving for <math>h</math> gives us <math>64 \Rightarrow \boxed{B}</math> | + | Let the height of the taller tree be <math>h</math> and let the height of the smaller tree be <math>h-16</math>. Since the ratio of the smaller tree to the larger tree is <math>\frac{3}{4}</math>, we have <math>\frac{h-16}{h}=\frac{3}{4}</math>. Solving for <math>h</math> gives us <math>h=64 \Rightarrow \boxed{\textbf{(B)}\ 64}</math> |
Revision as of 20:36, 11 March 2012
Problem
The top of one tree is 
feet higher than the top of another tree. The heights of the two trees are in the ratio 
. In feet, how tall is the taller tree?
Solution
Let the height of the taller tree be 
and let the height of the smaller tree be 
. Since the ratio of the smaller tree to the larger tree is 
, we have 
. Solving for gives us 
