Difference between revisions of "2015 AMC 10B Problems/Problem 4"
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Four siblings ordered an extra large pizza. Alex ate <math>\frac15</math>, Beth <math>\frac13</math>, and Cyril <math>\frac14</math> of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of pizza they consumed? | Four siblings ordered an extra large pizza. Alex ate <math>\frac15</math>, Beth <math>\frac13</math>, and Cyril <math>\frac14</math> of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of pizza they consumed? | ||
− | <math>\textbf{(A) } \text{Alex, Beth, Cyril, Dan}</math> | + | <math>\textbf{(A) } \text{Alex, Beth, Cyril, Dan}</math> <br> |
− | <math>\textbf{(B) } \text{Beth, Cyril, Alex, Dan}</math> | + | <math>\textbf{(B) } \text{Beth, Cyril, Alex, Dan}</math> <br> |
+ | <math>\textbf{(C) } \text{Beth, Cyril, Dan, Alex}</math> <br> | ||
+ | <math>\textbf{(D) } \text{Beth, Dan, Cyril, Alex}</math> <br> | ||
+ | <math>\textbf{(E) } \text{Dan, Beth, Cyril, Alex}</math> <br> | ||
− | + | ==Solution== | |
− | |||
− | <math>\textbf{( | + | Let the pizza have <math>60</math> slices, since the least common multiple of <math>(5,3,4)=60</math>. Therefore, Alex ate <math>\frac{1}{5}\times60=12</math> slices, Beth ate <math>\frac{1}{3}\times60=20</math> slices, and Cyril ate <math>\frac{1}{4}\times60=15</math> slices. Dan must have eaten <math>60-(12+20+15)=13</math> slices. In decreasing order, we see the answer is <math>\boxed{\textbf{(C) }\text{Beth, Cyril, Dan, Alex}}</math>. |
− | ==Solution== | + | ==Video Solution== |
+ | https://youtu.be/PW6_dcQbhyE | ||
− | + | ~savannahsolver | |
==See Also== | ==See Also== | ||
{{AMC10 box|year=2015|ab=B|num-b=3|num-a=5}} | {{AMC10 box|year=2015|ab=B|num-b=3|num-a=5}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 13:09, 18 June 2020
Contents
Problem 4
Four siblings ordered an extra large pizza. Alex ate , Beth , and Cyril of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of pizza they consumed?
Solution
Let the pizza have slices, since the least common multiple of . Therefore, Alex ate slices, Beth ate slices, and Cyril ate slices. Dan must have eaten slices. In decreasing order, we see the answer is .
Video Solution
~savannahsolver
See Also
2015 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 |
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