2014 AMC 10B 第 4 题

Question

Susie 买了

4

个松饼和

3

根香蕉。Calvin 买了

2

个松饼和

16

根香蕉，花费是 Susie 的两倍。一个松饼的价格是香蕉的多少倍？

Susie pays for

4

muffins and

3

bananas. Calvin spends twice as much paying for

2

muffins and

16

bananas. A muffin is how many times as expensive as a banana?

\dfrac{3}{2}

\dfrac{5}{3}

\dfrac{7}{4}

2

\dfrac{13}{4}

设松饼和香蕉的价格为变量。

Let the muffin and banana prices be variables

先使用 Calvin 花费是 Susie 两倍这个条件，再求价格比。

Use Calvin spent twice Susie’s amount before solving the ratio

设一个松饼价格为

m

，一根香蕉价格为

b

。

\begin{aligned} 2(4m+3b) &= 16b + 2m\\ 8m+6b &= 16b + 2m \\ 10b &= 6m\\ m &= \dfrac 53 b\end{aligned}\text{。}

所以正确答案是 B。

Let the price for a muffin be

m

and let the price for a banana be

b.

Then,

\begin{aligned} 2(4m+3b) &= 16b + 2m\\ 8m+6b &= 16b + 2m \\ 10b &= 6m\\ m &= \dfrac 53 b.\end{aligned}

Thus, the correct answer is B .

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