1988 AHSME Problems/Problem 26
Problem
Suppose that and
are positive numbers for which
What is the value of ?
Solution
We can rewrite the equation as . Then, the system can be split into 3 pairs:
,
, and
. Cross-multiplying in the first two, we obtain:
and
Adding these equations results in:
which simplifies to
Dividing by
on both sides gives:
. We set the desired value,
to
and substitute it into our equation:
which is solved to get our answer:
.
See also
1988 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 25 |
Followed by Problem 27 | |
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