Difference between revisions of "2008 AMC 12B Problems/Problem 3"
(New page: ==Problem 3== A semipro baseball league has teams with <math>21</math> players each. League rules state that a player must be paid at least <math>15,000</math> dollars, and that the total ...) |
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| − | ==Problem | + | ==Problem== |
A semipro baseball league has teams with <math>21</math> players each. League rules state that a player must be paid at least <math>15,000</math> dollars, and that the total of all players' salaries for each team cannot exceed <math>700,000</math> dollars. What is the maximum possiblle salary, in dollars, for a single player? | A semipro baseball league has teams with <math>21</math> players each. League rules state that a player must be paid at least <math>15,000</math> dollars, and that the total of all players' salaries for each team cannot exceed <math>700,000</math> dollars. What is the maximum possiblle salary, in dollars, for a single player? | ||
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We want to find the maximum any player could make, so assume that everyone else makes the minimum possible and that the combined salaries total the maximum of <math>700,000</math> | We want to find the maximum any player could make, so assume that everyone else makes the minimum possible and that the combined salaries total the maximum of <math>700,000</math> | ||
| − | <math>700,000 = 20 * 15,000 + x | + | <math>700,000 = 20 * 15,000 + x</math> |
| − | </math> | ||
| − | The | + | <math>x = 400,000</math> |
| + | |||
| + | The maximum any player could make is <math>400,000</math> dollars <math>\Rightarrow C</math> | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC12 box|year=2008|ab=B|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 12:47, 15 February 2021
Problem
A semipro baseball league has teams with 
players each. League rules state that a player must be paid at least 
dollars, and that the total of all players' salaries for each team cannot exceed 
dollars. What is the maximum possiblle salary, in dollars, for a single player?
Solution
We want to find the maximum any player could make, so assume that everyone else makes the minimum possible and that the combined salaries total the maximum of
The maximum any player could make is 
dollars 
See Also
| 2008 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 2 |
Followed by Problem 4 |
| 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 AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
