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?
Answer Choices:
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Solution:
Let the numbers be , and . Then , and . From the first two equations it follows that . From the third equation it follows that , which gives . Hence , and .
The problems on this page are the property of the MAA's American Mathematics Competitions