Difference between revisions of "2022 AMC 8 Problems/Problem 6"
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Revision as of 13:07, 11 June 2023
Contents
Problem
Three positive integers are equally spaced on a number line. The middle number is 
and the largest number is 
times the smallest number. What is the smallest of these three numbers?
Solution 1
Let the smallest number be 
It follows that the largest number is 
Since 
and 
are equally spaced on a number line, we have
~MRENTHUSIASM
Solution 2
Let the common different of the arithmetic sequence be 
. Consequently, the smallest number is 
and the largest number is 
. As the largest number is times the smallest number, 
. Finally, we find that the smallest number is 
.
~MathFun1000
Video Solution
~STEMbreezy
Video Solution
~savannahsolver
Video Solution
https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=409
~Interstigation
See Also
| 2022 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
