Problem: 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 Choices:
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Solution:
Let be Ann's present age, and let be Barbara's present age. Then for such that " for such that ." Since, also, , the quantities and are solutions to the equations
These equations may be conveniently solved by using the first two equations to find and in terms of and substituting the results into the third and fourth equations; .