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# Competition Math

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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?

Nov 7, 2019

#1
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She has to pick up 30 toys.

Mia's mom puts 3 toys, and mia takes 2 toys out.

So 3 - 2 = ONE TOY being put into the box EVERY 30 seconds.

Since one toy is being put into the box every 30 seconds.

It will take 30 * 30 = 900 seconds.

900/60 = 15 minutes

oh the burden of being a parent, good thing for me I am still a youngling

Nov 7, 2019
#3
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oops! At least you know what NOT to do.

CalculatorUser  Nov 8, 2019
#2
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soultion1: Every 30 seconds 3-2=1 toys are put in the box, so after 27\cdot30 seconds, there will be 27 toys in the box. Mia's mom will then put 3 toys into the box and we have our total amount of time to be 27\cdot30+30=840 seconds, which equals 14 minutes

soultion2: Though Mia's mom places 3 toys every 30 seconds, Mia takes out 2 toys right after. Therefore, after 30 seconds, the two have collectively placed 1 toy into the box. Therefore by 13.5 minutes, the two would have placed 27 toys into the box. Therefore, at 14 minutes, the two would have placed 30 toys into the box. Though Mia may take 2 toys out right after, the number of toys in the box first reaches 30 by 14 minutes

Nov 7, 2019
edited by tomsun  Nov 7, 2019