Problem:
Mia is "helping" her mom pick up toys that are strewn on the floor. Mia's mom manages to put toys into the toy box every seconds, but each time immediately after those seconds have elapsed, Mia takes toys out of the box. How much time, in minutes, will it take Mia and her mom to put all toys into the box for the first time?
Answer Choices:
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Solution:
After exactly half a minute there will be toys in the box and toys outside the box. During the next half-minute, Mia takes toys out and her mom puts toys into the box. This means that during this half-minute the number of toys in the box was increased by . 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 half-minutes, which is minutes, to complete the task.
The problems on this page are the property of the MAA's American Mathematics Competitions