AMC10 2014 B

AMC10 2014 B · Q4

AMC10 2014 B · Q4. It mainly tests Linear equations, Systems of equations.

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 a muffin cost $m$ dollars and a banana cost $b$ dollars. Then $2(4m + 3b) = 2m + 16b$, and simplifying gives $m = \frac{5}{3}b$.

设一个松饼价格 $m$ 美元，一个香蕉价格 $b$ 美元。那么 $2(4m + 3b) = 2m + 16b$，化简得 $m = \frac{5}{3}b$。

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