1996 AJHSME Problems/Problem 23
Contents
[hide]Problem
The manager of a company planned to distribute a bonus to each employee from the company fund, but the fund contained less than what was needed. Instead the manager gave each employee a bonus and kept the remaining in the company fund. The amount of money in the company fund before any bonuses were paid was
Solution 1
Let be the number of people in the company, and be the amount of money in the fund.
The first sentence states that
The second sentence states that
Subtracing the second equation from the first, we get , leading to
Plugging that number into the first equation gives , leading to , which is answer .
Solution 2
Since the company must employ a whole number of employees, the amount of money in the fund must be dollars less than a multiple of . Only options and satisfy that requirement.
Additionally, the number must be more than a multiple of . Since , the only number that is more than a multiple of out of options and is option .
(Option is also more than a multiple of , but it was eliminated previously.)
See Also
1996 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.