Difference between revisions of "2017 AMC 10A Problems/Problem 4"
m (→Solution) |
Nitropixel (talk | contribs) (→Video Solutions) |
||
(13 intermediate revisions by 8 users not shown) | |||
Line 6: | Line 6: | ||
==Solution== | ==Solution== | ||
− | Every <math>30</math> seconds <math>3 | + | 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. |
− | + | 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 | ||
+ | |||
+ | https://youtu.be/1F0IB0y6578 | ||
+ | |||
+ | ~savannahsolver | ||
==See also== | ==See also== |
Latest revision as of 15:15, 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.