2017 AMC 10 A
Complete problem set with solutions and individual problem pages
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? (2017 AMC 10A Problem, Question#4)
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Every seconds toys are put in the box, so after seconds there will be toys in the box. Mia's mom will then put toys into to the box and we have our total amount of time to be seconds, which equals minutes.
Though Mia's mom places toys every seconds, Mia takes out toys right after. Therefore, after seconds, the two have collectively placed toy into the box. Therefore by minutes, the two would have placed toys into the box. Therefore, at minutes, the two would have placed toys into the box. Though Mia may take toys out right after, the number of toys in the box first reaches by minutes.
