2014 AMC 10B Problems/Problem 4: Difference between revisions
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==Problem== | ==Problem== | ||
Susie pays for <math>4</math> muffins and <math>3</math> bananas. Calvin spends twice as much paying for <math>2</math> muffins and <math>16</math> bananas. A muffin is how many times as expensive as a banana? | |||
<math> \textbf {(A) } \frac{3}{2} \qquad \textbf {(B) } \frac{5}{3} \qquad \textbf {(C) } \frac{7}{4} \qquad \textbf {(D) } 2 \qquad \textbf {(E) } \frac{13}{4}</math> | |||
==Solution== | ==Solution== | ||
Let <math>m</math> be the cost of a muffin and <math>b</math> be the cost of a banana. From the given information, <cmath>2m+16b=2(4m+3b)=8m+6b\Rightarrow 10b=6m\Rightarrow m=\frac{10}{6}b=\boxed{\frac{5}{3}\rightarrow \text{(B)}}</cmath>. | |||
==Video Solution (CREATIVE THINKING)== | |||
https://youtu.be/_AvJzq4QiUg | |||
~Education, the Study of Everything | |||
==Video Solution== | |||
https://youtu.be/7_-ZvunSC8w | |||
~savannahsolver | |||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2014|ab=B| | {{AMC10 box|year=2014|ab=B|num-b=3|num-a=5}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 21:36, 26 September 2023
Problem
Susie pays for 
muffins and 
bananas. Calvin spends twice as much paying for 
muffins and 
bananas. A muffin is how many times as expensive as a banana?
Solution
Let 
be the cost of a muffin and 
be the cost of a banana. From the given information, ![\[2m+16b=2(4m+3b)=8m+6b\Rightarrow 10b=6m\Rightarrow m=\frac{10}{6}b=\boxed{\frac{5}{3}\rightarrow \text{(B)}}\]](http://latex.artofproblemsolving.com/9/b/0/9b04ffdd625fd7e0c6e1a2b193eedc4835807573.png)
.
Video Solution (CREATIVE THINKING)
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
| 2014 AMC 10B (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. 
