2017 AMC 10A Problems/Problem 4

Revision as of 13:11, 3 February 2021 by Scrabbler94 (talk | contribs) (combine solutions 1 and 2 as they are essentially the same. also clarify that the number of toys increases by 1; not necessarily "1 toy is placed in the box" since different toys can be put in and taken out.)

Problem

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?

$\textbf{(A)}\ 13.5\qquad\textbf{(B)}\ 14\qquad\textbf{(C)}\ 14.5\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 15.5$

Solution

Every $30$ seconds, $3$ toys are put in the box and $2$ toys are taken out, so the number of toys increases by $3-2=1$ every 30 seconds. Then after $27 \times 30 = 810$ seconds (or $13 \frac{1}{2}$ minutes), there are 27 toys in the box. Mia's mom will then put $3$ toys into the box after 30 more seconds, so the total time taken is $27\cdot30+30=840$ seconds, or $\boxed{(\textbf{B})\ 14}$ minutes.

Video Solution

https://youtu.be/str7kmcRMY8

https://youtu.be/1F0IB0y6578

~savannahsolver

See also

2017 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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