Difference between revisions of "2017 AMC 10A Problems/Problem 4"
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==Solution== | ==Solution== | ||
| − | Every <math>30</math> seconds, <math>3</math> toys are put in the box and <math>2</math> toys are taken out, so the number of toys increases by <math>3-2=1</math> every <math>30</math> seconds. Then after <math>27 \times 30 = 810</math> seconds (or <math>13 \frac{1}{2}</math> minutes), there are <math>27</math> toys in the box. Mia's mom will then put the remaining <math>3</math> toys into the box after <math>30</math> more seconds, so the total time taken is <math>27\times 30+30=840</math> seconds, or <math>\boxed{(\textbf{B})\ 14}</math> minutes. | + | Every <math>30</math> seconds, <math>3</math> toys are put in the box and <math>2</math> toys are taken out, so the number of toys in the box increases by <math>3-2=1</math> every <math>30</math> seconds. Then after <math>27 \times 30 = 810</math> seconds (or <math>13 \frac{1}{2}</math> minutes), there are <math>27</math> toys in the box. Mia's mom will then put the remaining <math>3</math> toys into the box after <math>30</math> more seconds, so the total time taken is <math>27\times 30+30=840</math> seconds, or <math>\boxed{(\textbf{B})\ 14}</math> minutes. |
| − | ==Video | + | Note: During the last time Mia's mom will complete picking up the 30 toys(before Mia can take 2 out) which is the reason that you calculate up to 27 and then the rest. |
| + | |||
| + | ==Video Solutions== | ||
https://youtu.be/str7kmcRMY8 | https://youtu.be/str7kmcRMY8 | ||
| + | -Video Solution by TheBeautyOfMath | ||
https://youtu.be/1F0IB0y6578 | https://youtu.be/1F0IB0y6578 | ||
Latest revision as of 14:15, 26 August 2022
Contents
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
Every seconds, toys are put in the box and toys are taken out, so the number of toys in the box increases by 
every seconds. Then after 
seconds (or 
minutes), there are 
toys in the box. Mia's mom will then put the remaining toys into the box after more seconds, so the total time taken is 
seconds, or 
minutes.
Note: During the last time Mia's mom will complete picking up the 30 toys(before Mia can take 2 out) which is the reason that you calculate up to 27 and then the rest.
Video Solutions
https://youtu.be/str7kmcRMY8 -Video Solution by TheBeautyOfMath
~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. 
