2019 AMC 10A Problems/Problem 3
Contents
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
Solution
Solution 1
Let be the age of Ana and be the age of Bonita. Then,
and
Substituting the second equation into the first gives us
By using difference of squares and dividing, Moreover,
The answer is
Solution 2 (Guess and Check)
Simple guess and check works. Start with all the square numbers - , , , , , , etc. (probably stop at around since at that point it wouldn't make sense). If Ana is , then Bonita is , so in the previous year, Ana's age was times greater than Bonita's. If Ana is , then Bonita is , and Ana's age was times greater than Bonita's in the previous year, as required. The difference in the ages is
Solution 3 (Answer Choices)
The second sentence of the problem says that Ana's age was once times Bonita's age. Therefore, the difference of the ages must be divisible by The only answer choice which is divisible by is
- awesome_weisur
Video Solution 1
Education, The Study of Everything
Video Solution 2
~savannahsolver
See Also
2019 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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All AMC 10 Problems and Solutions |
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