AMC12 2018 B

AMC12 2018 B · Q6

AMC12 2018 B · Q6. It mainly tests Ratios & proportions, Unit conversion.

Suppose S cans of soda can be purchased from a vending machine for Q quarters. Which of the following expressions describes the number of cans of soda that can be purchased for D dollars, where 1 dollar is worth 4 quarters?

假设用 Q 个25美分硬币可以从自动售货机购买 S 罐苏打水。那么用 D 美元可以购买多少罐苏打水，其中1美元等于4个25美分硬币？

(A) \frac{4DQ}{S} \frac{4DQ}{S}

(B) \frac{4DS}{Q} \frac{4DS}{Q}

(D) \frac{DQ}{4S} \frac{DQ}{4S}

(E) \frac{DS}{4Q} \frac{DS}{4Q}

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): The cost of 1 can is $\frac{Q}{S}$ quarters, which is $\frac{Q}{4S}$ dollars. Hence the number of cans that can be purchased with $D$ dollars is $$ \frac{D}{\left(\frac{Q}{4S}\right)}=\frac{4DS}{Q}. $$

答案（B）：1 罐的价格是 $\frac{Q}{S}$ 个 25 美分（quarters），即 $\frac{Q}{4S}$ 美元。因此，用 $D$ 美元可以买到的罐数为 $$ \frac{D}{\left(\frac{Q}{4S}\right)}=\frac{4DS}{Q}. $$

Topics