1976 AMC 12 Problem 29
Attempt Problem 29 of the 1976 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1976 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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
Answer: B
Small Hint:
Let Ann’s and Barbara’s present ages be and with
Big Hint:
Translate each “when” by subtracting the same elapsed time from both ages
Solution:
Let Ann’s and Barbara’s present ages be and and let their constant age difference be At the first referenced time Ann was so Barbara was At the earlier referenced time Ann was that age so Barbara was The final clause says this last age was Hence which gives Together with this yields and
Therefore, the correct answer is B.
Problem 29 in Other Years
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