2022 AMC 8 Problems/Problem 13
Problem
How many positive integers can fill the blank in the sentence below?
“One positive integer is _____ more than twice another, and the sum of the two numbers is .”
- _=_=Solution=_=_****
Let and
be positive integers such that
and
It follows that
for some positive integer
We wish to find the number of possible values for
By substitution, we have from which
Note that
each generate a positive integer for
so there are
possible values for
~MRENTHUSIASM
Video Solution
https://youtu.be/Ij9pAy6tQSg?t=1110
~Interstigation
See Also
2022 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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All AJHSME/AMC 8 Problems and Solutions |
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