2017 AMC 10A Problems/Problem 4: Difference between revisions
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==Problem== | ==Problem== | ||
Mia is “helping” her mom pick up <math>30</math> toys that are strewn on the floor. Mia’s mom manages to put <math>3</math> toys into the toy box every <math>30</math> seconds, but each time immediately after those <math>30</math> seconds have elapsed, Mia takes <math>2</math> toys out of the box. How much time, in minutes, will it take Mia and her mom to put all <math>30</math> toys into the box for the first time? | Mia is “helping” her mom pick up <math>30</math> toys that are strewn on the floor. Mia’s mom manages to put <math>3</math> toys into the toy box every <math>30</math> seconds, but each time immediately after those <math>30</math> seconds have elapsed, Mia takes <math>2</math> toys out of the box. How much time, in minutes, will it take Mia and her mom to put all <math>30</math> toys into the box for the first time? | ||
<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== | ||
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 to 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> | 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 to 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> | ||
==See | ==See also== | ||
{{AMC10 box|year=2017|ab=A|num-b=3|num-a=5}} | {{AMC10 box|year=2017|ab=A|num-b=3|num-a=5}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 18:02, 8 February 2017
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, so after 
seconds there will be 
toys in the box. Mia's mom will then put toys into to the box and we have our total amount of time to be 
seconds, which equals 
minutes. 
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 | ||
These problems are copyrighted © by the Mathematical Association of America. 
