# Difference between revisions of "2017 AMC 10A Problems/Problem 4"

## 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

~savannahsolver

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 