Difference between revisions of "2014 AMC 8 Problems/Problem 2"
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| + | ==Problem== | ||
Paul owes Paula <math>35</math> cents and has a pocket full of <math>5</math>-cent coins, <math>10</math>-cent coins, and <math>25</math>-cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her? | Paul owes Paula <math>35</math> cents and has a pocket full of <math>5</math>-cent coins, <math>10</math>-cent coins, and <math>25</math>-cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her? | ||
<math>\textbf{(A) }1\qquad\textbf{(B) }2\qquad\textbf{(C) }3\qquad\textbf{(D) }4\qquad \textbf{(E) }5</math> | <math>\textbf{(A) }1\qquad\textbf{(B) }2\qquad\textbf{(C) }3\qquad\textbf{(D) }4\qquad \textbf{(E) }5</math> | ||
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| + | ==Solution== | ||
| + | The fewest amount of coins that can be used is <math>2</math> (a quarter and a dime). The greatest amount is <math>7</math>, if he only uses nickels. Therefore we have <math>7-2=\boxed{\textbf{(E)}~5}</math>. | ||
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| + | ==Video Solution (CREATIVE THINKING)== | ||
| + | https://youtu.be/Gm7gDXHjnUU | ||
| + | |||
| + | ~Education, the Study of Everything | ||
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| + | ==Video Solution== | ||
| + | https://youtu.be/OOdK-nOzaII?t=454 | ||
| + | |||
| + | https://youtu.be/scOob5X-l6g | ||
| + | |||
| + | ~savannahsolver | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2014|num-b=1|num-a=3}} | {{AMC8 box|year=2014|num-b=1|num-a=3}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 00:33, 12 December 2023
Problem
Paul owes Paula 
cents and has a pocket full of 
-cent coins, 
-cent coins, and 
-cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her?
Solution
The fewest amount of coins that can be used is 
(a quarter and a dime). The greatest amount is 
, if he only uses nickels. Therefore we have 
.
Video Solution (CREATIVE THINKING)
~Education, the Study of Everything
Video Solution
https://youtu.be/OOdK-nOzaII?t=454
~savannahsolver
See Also
| 2014 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
