Difference between revisions of "2010 AMC 10B Problems/Problem 4"
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<cmath>\frac{1(1+1)}{2} + \frac{2(2+1)}{2} + \frac{3(3+1)}{2} = \frac{2}{2} + \frac{6}{2} + \frac{12}{2} = 1+3+6= \boxed{\textbf{(C)} 10}</cmath> | <cmath>\frac{1(1+1)}{2} + \frac{2(2+1)}{2} + \frac{3(3+1)}{2} = \frac{2}{2} + \frac{6}{2} + \frac{12}{2} = 1+3+6= \boxed{\textbf{(C)} 10}</cmath> | ||
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+ | ==Video Solution== | ||
+ | https://youtu.be/49jID-0tszU | ||
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+ | -Education, the Study of Everything | ||
==Video Solution== | ==Video Solution== |
Latest revision as of 15:59, 1 August 2022
Problem
For a real number , define to be the average of and . What is ?
Solution
The average of two numbers, and , is defined as . Thus the average of and would be . With that said, we need to find the sum when we plug, , and into that equation. So:
Video Solution
-Education, the Study of Everything
Video Solution
https://youtu.be/uAc9VHtRRPg?t=209
~IceMatrix
See Also
2010 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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.