Difference between revisions of "2017 AMC 10A Problems/Problem 4"
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<math>\textbf{(A)}\ 13.5\qquad\textbf{(B)}\ 14\qquad\textbf{(C)}\ 14.5\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 15.5</math> | <math>\textbf{(A)}\ 13.5\qquad\textbf{(B)}\ 14\qquad\textbf{(C)}\ 14.5\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 15.5</math> | ||
− | ==Solution== | + | ==Solution 1== |
− | Every <math>30</math> seconds <math>3-2=1</math> toys are put in the box, so after <math>27\cdot30</math> seconds there will be <math>27</math> toys in the box. Mia's mom will then put <math>3</math> toys into | + | Every <math>30</math> seconds, <math>3-2=1</math> toys are put in the box, so after <math>27\cdot30</math> seconds, there will be <math>27</math> toys in the box. Mia's mom will then put <math>3</math> toys into the box, and we have our total amount of time to be <math>27\cdot30+30=840</math> seconds, which equals <math>14</math> minutes. <math>\boxed{(\textbf{B})\ 14}</math> |
==Solution 2== | ==Solution 2== |
Revision as of 12:08, 31 January 2021
Problem
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?
Solution 1
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 the box, and we have our total amount of time to be
seconds, which equals
minutes.
Solution 2
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.
Video Solution
~savannahsolver
See also
2017 AMC 10A (Problems • Answer Key • Resources) | ||
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.