AMC12 2014 B

AMC12 2014 B · Q4

AMC12 2014 B · Q4. It mainly tests Systems of equations, Ratios & proportions.

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?

Susie 买了 4 个松饼和 3 个香蕉。Calvin 花费是 Susie 的两倍，买了 2 个松饼和 16 个香蕉。一个松饼比一个香蕉贵多少倍？

(A) \frac{3}{2} \frac{3}{2}

(B) \frac{5}{3} \frac{5}{3}

(D) 2 2

(E) \frac{13}{4} \frac{13}{4}

Answer

Correct choice: (B)

正确答案：（B）

Solution

Let $m$ be the cost of a muffin and $b$ the cost of a banana in dollars. Then $2m + 16b = 2(4m + 3b)$, which simplifies to $m = \frac{5}{3}b$.

设松饼价格为 $m$ 美元，香蕉价格为 $b$ 美元。那么 $2m + 16b = 2(4m + 3b)$，化简得 $m = \frac{5}{3}b$。

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