Difference between revisions of "2021 AMC 10B Problems/Problem 5"
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Next, look at the two cousins' ages that multiply to <math>30</math>. Since the ages must be single-digit, the only ages that work are <math>5 \text{ and } 6.</math> Remembering that all the ages must all be distinct, the only solution that works is when the ages are <math>3, 8</math> and <math>5, 6</math>. | Next, look at the two cousins' ages that multiply to <math>30</math>. Since the ages must be single-digit, the only ages that work are <math>5 \text{ and } 6.</math> Remembering that all the ages must all be distinct, the only solution that works is when the ages are <math>3, 8</math> and <math>5, 6</math>. | ||
− | We are required to find the sum of the ages, which is <cmath>3 + 8 + 5 + 6 = \boxed{(B) | + | We are required to find the sum of the ages, which is <cmath>3 + 8 + 5 + 6 = \boxed{\textbf{(B)} ~22}.</cmath> |
-[[User:PureSwag|PureSwag]] | -[[User:PureSwag|PureSwag]] | ||
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~IceMatrix | ~IceMatrix | ||
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+ | ==Video Solution by Interstigation== | ||
+ | https://youtu.be/DvpN56Ob6Zw?t=358 | ||
+ | |||
+ | ~Interstigation | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/cQC4YORt3OU | ||
+ | |||
+ | ~Education, the Study of Everything | ||
== See Also == | == See Also == |
Latest revision as of 17:18, 16 August 2022
Contents
[hide]Problem
The ages of Jonie's four cousins are distinct single-digit positive integers. Two of the cousins' ages multiplied together give , while the other two multiply to . What is the sum of the ages of Jonie's four cousins?
Solution
First look at the two cousins' ages that multiply to . Since the ages must be single-digit, the ages must either be or
Next, look at the two cousins' ages that multiply to . Since the ages must be single-digit, the only ages that work are Remembering that all the ages must all be distinct, the only solution that works is when the ages are and .
We are required to find the sum of the ages, which is
Video Solution by OmegaLearn (Using Factors)
~ pi_is_3.14
Video Solution by TheBeautyofMath
https://youtu.be/gLahuINjRzU?t=857
~IceMatrix
Video Solution by Interstigation
https://youtu.be/DvpN56Ob6Zw?t=358
~Interstigation
Video Solution
~Education, the Study of Everything
See Also
2021 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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.