Difference between revisions of "2010 AMC 8 Problems/Problem 11"
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==Solution 2 == | ==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 | + | 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 B(64) |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2010|num-b=10|num-a=12}} | {{AMC8 box|year=2010|num-b=10|num-a=12}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 00:22, 4 November 2016
Contents
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
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 B(64)
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.