1970 AHSME Problems/Problem 35
Problem
A retiring employee receives an annual pension proportional to the square root of the number of years of his service. Had he served years more, his pension would have been dollars greater, whereas had he served years more , his pension would have been dollars greater than the original annual pension. Find his annual pension in terms of and .
Solution
Note the original pension as , where is the number of years served. Then, based on the problem statement, two equations can be set up.
Square the first equation to get
Because both sides have , they cancel out. Similarly, the second equation will become Then, can be multiplied to the second equation and can be multiplied to the first equation so that the left side of both equations becomes . Finally, by setting the equations equal to each other, Isolate to get .
See also
1970 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 34 |
Followed by Problem 35 | |
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