Problem:
Ana and Bonita were born on the same date in different years, years apart. Last year Ana was times as old as Bonita. This year Ana's age is the square of Bonita's age. What is ?
Answer Choices:
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Solution:
If denotes Bonita's age last year, then Ana's age last year was . This year Bonita's age is , and Ana's age is . So the given condition is . This quadratic equation simplifies to . Because the two girls were born in different years, , so . Last year Bonita was and Ana was , so they were born years apart. As a check, note that Ana's age this year, , is indeed the square of Bonita's age this year, .
The problems on this page are the property of the MAA's American Mathematics Competitions