AMC12 2012 A

AMC12 2012 A · Q2

AMC12 2012 A · Q2. It mainly tests Fractions, Work problems.

Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes?

Cagney 每 20 秒可以给一个纸杯蛋糕上糖霜，Lacey 每 30 秒可以给一个纸杯蛋糕上糖霜。他们一起工作，5 分钟内可以给多少个纸杯蛋糕上糖霜？

(A) 10 10

(B) 15 15

(D) 25 25

(E) 30 30

Answer

Correct choice: (D)

正确答案：（D）

Solution

Cagney can frost one in $20$ seconds, and Lacey can frost one in $30$ seconds. Working together, they can frost one in $\frac{20\cdot30}{20+30} = \frac{600}{50} = 12$ seconds. In $300$ seconds ($5$ minutes), they can frost $\boxed{\textbf{(D)}\ 25}$ cupcakes.

Cagney 给一个上糖霜需要 $20$ 秒，Lacey 给一个上糖霜需要 $30$ 秒。一起工作时，他们给一个上糖霜需要 $\frac{20\cdot30}{20+30} = \frac{600}{50} = 12$ 秒。在 $300$ 秒（$5$ 分钟）内，他们可以给 $\boxed{\textbf{(D)}\ 25}$ 个纸杯蛋糕上糖霜。

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