Difference between revisions of "1976 AHSME Problems/Problem 29"
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Latest revision as of 17:10, 21 April 2021
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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