AMC8 2010

AMC8 2010 · Q11

AMC8 2010 · Q11. It mainly tests Linear equations, Ratios & proportions.

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 3 : 4. 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。两棵树的高度之比为3:4。较高的树有多高（英尺）？

(A) 48 48

(B) 64 64

(D) 96 96

(E) 112 112

Answer

Correct choice: (B)

正确答案：（B）

Solution

Let the height of the taller tree be $h$ and let the height of the smaller tree be $h-16$. Since the ratio of the smaller tree to the larger tree is $\frac{3}{4}$, we have $\frac{h-16}{h}=\frac{3}{4}$. Solving for $h$ gives us $h=64 \Rightarrow \boxed{\textbf{(B)}\ 64}$

设较高的树的高度为$h$，较矮的树的高度为$h-16$。由于较矮树与较高树的比值为$\frac{3}{4}$，有$\frac{h-16}{h}=\frac{3}{4}$。解得$h=64 \Rightarrow \boxed{\textbf{(B)}\ 64}$

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