2022 AMC 10A Problems/Problem 3
Contents
Problem
The sum of three numbers is The first number is times the third number, and the third number is less than the second number. What is the absolute value of the difference between the first and second numbers?
Solution 1
Let be the third number. It follows that the first number is and the second number is
We have from which
Therefore, the first number is and the second number is Their absolute value of the difference is
~MRENTHUSIASM
Solution 2
Solve this using a system of equations. Let and be the three numbers, respectively. We get three equations: Rewriting the third equation gives us so we can substitute as and as
Therefore, we get Substituting 7 in for gives us and
So, the answer is
~alexdapog A-A
Solution 3
In accordance with Solution 2, vladimir.shelomovskii@gmail.com, vvsss
Video Solution 1 (Quick and Easy)
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Video Solution 2
~Charles3829
Video Solution 3 (2 minutes)
https://youtu.be/7yAh4MtJ8a8?si=Xpc2h85yyqEMOnVb&t=322
~Math-x
See Also
2022 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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 |
2022 AMC 12A (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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.