AMC 8 2010 Problem 11
AMC8 2010 年第 11 题
比与比例★★★☆☆
The top of one tree is 16 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?
一棵树的顶部比另一棵树的顶部高 16 英尺。这两棵树的高度之比是 3：4。那么较高的那棵树高多少英尺？
- A.48
- B.64
- C.80
- D.96
- E.112
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
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 in the ratio are consecutive (difference of 1), 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 . s + 16 = t, 3t = 4s. Solving by substitution, , , t=64. Assume the ratio is represented through . Then, 4x=3x+16, meaning x=16. Plug back into to get t=64 -N. Video by MathTalks https:
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