Difference between revisions of "2020 AMC 10A Problems/Problem 2"
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− | ==Problem | + | ==Problem== |
The numbers <math>3, 5, 7, a,</math> and <math>b</math> have an average (arithmetic mean) of <math>15</math>. What is the average of <math>a</math> and <math>b</math>? | The numbers <math>3, 5, 7, a,</math> and <math>b</math> have an average (arithmetic mean) of <math>15</math>. What is the average of <math>a</math> and <math>b</math>? | ||
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== Solution == | == Solution == | ||
− | The arithmetic mean of the numbers <math>3, 5, 7, a,</math> and <math>b</math> is equal to <math>\frac{3+5+7+a+b}{5}=\frac{15+a+b}{5}=15</math>. Solving for <math>a+b</math>, we get <math>a+b=60</math>. Dividing by <math>2</math> to find the average of the two numbers <math>a</math> and <math>b</math> gives <math>\frac{60}{2}=\boxed{\ | + | The arithmetic mean of the numbers <math>3, 5, 7, a,</math> and <math>b</math> is equal to <math>\frac{3+5+7+a+b}{5}=\frac{15+a+b}{5}=15</math>. Solving for <math>a+b</math>, we get <math>a+b=60</math>. Dividing by <math>2</math> to find the average of the two numbers <math>a</math> and <math>b</math> gives <math>\frac{60}{2}=\boxed{\textbf{(C) }30}</math>. |
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+ | ==Video Solution== | ||
+ | |||
+ | Education, The Study of Everything | ||
+ | |||
+ | https://youtu.be/e8Qfe5GpEUg | ||
+ | |||
+ | https://youtu.be/WUcbVNy2uv0 | ||
+ | |||
+ | ~IceMatrix | ||
+ | |||
+ | https://www.youtube.com/watch?v=7-3sl1pSojc | ||
+ | |||
+ | ~bobthefam | ||
+ | |||
+ | https://youtu.be/zVppmKOvx_w | ||
+ | |||
+ | ~savannahsolver | ||
== See Also == | == See Also == | ||
− | {{AMC10 box|year=2020|ab=A| | + | {{AMC10 box|year=2020|ab=A|num-b=1|num-a=3}} |
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 11:40, 7 November 2020
Contents
Problem
The numbers and have an average (arithmetic mean) of . What is the average of and ?
Solution
The arithmetic mean of the numbers and is equal to . Solving for , we get . Dividing by to find the average of the two numbers and gives .
Video Solution
Education, The Study of Everything
~IceMatrix
https://www.youtube.com/watch?v=7-3sl1pSojc
~bobthefam
~savannahsolver
See Also
2020 AMC 10A (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 AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.