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Bunuel
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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?

(A) 13.5

(B) 14

(C) 14.5

(D) 15

(E) 15.5


Once we get 27 toys in the box, we hit our goal 30 seconds later.
The number of toys in the box increases by 1 every 30 seconds.
When do we get 27 toys in the box? 27*0.5 = 13.5 minutes.
30 seconds later is 14 minutes.

Answer choice B.
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We know that every 30 seconds Mia's mom puts 3 toys into the box, and immediately after that Mia takes 2 out. So every 30 seconds there is a growth of 1 more toy in the box.

As there are 30 toys we know that once the total number of toys in the box reaches 27, 30 seconds later the box will have all 30 toys.

Dividing 27 by 2 gives us the amount of minutes it will take to get to get to 27 toys as 30 seconds is half a minute: \(27÷2 = 13.5\)

It will take 13.5 minutes for there to be 27 toys in the box, and 30 seconds later there will be 30 toys in the box so in total it will take 14 minutes.
Answer B
It will take 13.5 minutes for there to be 27 toys in the box, and 30 seconds later there will be 30 toys in the box so in total it will take 14 minutes. --> here you are missing a step in between right? Mia removes 2 toys immediately after the 30 seconds. so the total comes out to be 27-2=25 after 13.5 minutes. After another 30 seconds, the total comes out to 25+3=28 not 30 right?

After 14 minutes, the immediate total is 28 and after Mia removes 2 toys the total is 28-2=26. After another 30 seconds, the total is 26+3=29 and after Mia removes 2 toys the total is 29-2=27. And at 15 minutes the immediate total is 27+3=30. So it takes 15 minutes to reach 30 toys for the first time not 14 minutes.
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