1976 AHSME Problems/Problem 29
Problem 29
Ann and Barbara were comparing their ages and found that Barbara is as old as Ann was when Barbara was as old as Ann had been when Barbara was half as old as Ann is. If the sum of their present ages is years, then Ann's age is
Solution
This problem is very wordy. Nonetheless, let and be Ann and Barbara's current ages, respectively. We are given that . Let equal the difference between their ages, so . Know that is constant because the difference between their ages will always be the same.
Now, let's tackle the equation: Ann's age when Barbara was Ann's age when Barbara was . When Barbara was years old, Ann was years old. So the equation becomes Ann's age when Barbara was . Adding on their age difference again, we get . Substitute back in for to get . Simplify: . Solving in terms of , we have . Substitute that back into the first equation of to get . Solve for , and the answer is . ~jiang147369
See Also
1976 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 28 |
Followed by Problem 30 | |
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