2003 AIME II Problems/Problem 1
Problem
The product of three positive integers is times their sum, and one of the integers is the sum of the other two. Find the sum of all possible values of .
Solution
Let the three integers be . and . Then . Since and are positive, so is one of so is one of so the sum of all possible values of is .
Video Solution by Sal Khan
https://www.youtube.com/watch?v=JPQ8cfOsYxo&list=PLSQl0a2vh4HCtW1EiNlfW_YoNAA38D0l4&index=7 - AMBRIGGS
See also
2003 AIME II (Problems • Answer Key • Resources) | ||
Preceded by First Question |
Followed by Problem 2 | |
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All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.