Difference between revisions of "2010 AMC 8 Problems/Problem 11"
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== 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>h=64 \Rightarrow \boxed{\textbf{(B)}\ 64}</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> | ||
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| + | ==See Also== | ||
| + | {{AMC8 box|year=2010|num-b=10|num-a=12}} | ||
Revision as of 16:37, 5 November 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 
See Also
| 2010 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
