AMC10 2017 A

AMC10 2017 A · Q4

AMC10 2017 A · Q4. It mainly tests Rates (speed), Patterns & sequences (misc).

Mia is “helping” her mom pick up 30 toys that are strewn on the floor. Mia’s mom manages to put 3 toys into the toy box every 30 seconds, but each time immediately after those 30 seconds have elapsed, Mia takes 2 toys out of the box. How much time, in minutes, will it take Mia and her mom to put all 30 toys into the box for the first time?

Mia 在“帮助”她妈妈捡起地板上散落的 30 个玩具。Mia 的妈妈每 30 秒放入 3 个玩具，但每当 30 秒刚过，Mia 立即从盒子里拿出 2 个玩具。Mia 和她妈妈第一次把所有 30 个玩具都放入盒子需要多少分钟？

(A) 13.5 13.5

(B) 14 14

(D) 15 15

(E) 15.5 15.5

Answer

Correct choice: (B)

正确答案：（B）

Solution

After exactly half a minute there will be 3 toys in the box and 27 toys outside the box. During the next half-minute, Mia takes 2 toys out and her mom puts 3 toys into the box. This means that during this half-minute the number of toys in the box was increased by 1. The same argument applies to each of the following half-minutes until all the toys are in the box for the first time. Therefore it takes 1 + 27 · 1 = 28 half-minutes, which is 14 minutes, to complete the task.

精确半分钟后，盒子里有 3 个玩具，外面有 27 个玩具。在接下来的半分钟里，Mia 拿出 2 个玩具，她妈妈放入 3 个玩具。这意味着在这半分钟里盒子里的玩具数增加了 1。同样论证适用于接下来的每个半分钟，直到所有玩具都放入盒子。因此需要 1 + 27 · 1 = 28 个半分钟，即 14 分钟完成任务。

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