Problem:
Tom's age is years, which is also the sum of the ages of his three children. His age years ago was twice the sum of their ages then. What is ?
Answer Choices:
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Solution:
Tom's age years ago was . The sum of his three children's ages at that time was . Therefore , so and . The conditions of the problem can be met, for example, if Tom's age is and the ages of his children are , and . In that case and .
The problems on this page are the property of the MAA's American Mathematics Competitions