2010 AMC 8 Problems/Problem 11
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 1(algebra 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
Solution 2
To answer this problem, you have to make it so that we have the same proportion as 3:4, but the difference between them is 16. Since the two numbers are consecutive, if we multiply both of them by 16, we would get a difference of 16 between them. So, it would be 48:64 and since we need to find the height of the taller tree, we get
Video by MathTalks
https://www.youtube.com/watch?v=6hRHZxSieKc
See Also
2010 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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