Difference between revisions of "2008 AMC 10B Problems/Problem 4"
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==Problem== | ==Problem== | ||
| − | A semipro baseball league has teams with 21 players each. League rules state that a player must be paid at least | + | A semipro baseball league has teams with 21 players each. League rules state that a player must be paid at least \$15,000 and that the total of all players' salaries for each team cannot exceed \$700,000. What is the maximum possible salary, in dollars, for a single player? |
<math>\mathrm{(A)}\ 270,000\qquad\mathrm{(B)}\ 385,000\qquad\mathrm{(C)}\ 400,000\qquad\mathrm{(D)}\ 430,000\qquad\mathrm{(E)}\ 700,000</math> | <math>\mathrm{(A)}\ 270,000\qquad\mathrm{(B)}\ 385,000\qquad\mathrm{(C)}\ 400,000\qquad\mathrm{(D)}\ 430,000\qquad\mathrm{(E)}\ 700,000</math> | ||
==Solution== | ==Solution== | ||
| − | {{ | + | The maximum occurs when 20 players get the minimum wage and the total of all players' salaries is 700000. That is when one player gets <math>700000-15000*20=400000\Rightarrow \boxed{\mathrm{(C)}}</math>. |
==See also== | ==See also== | ||
{{AMC10 box|year=2008|ab=B|num-b=3|num-a=5}} | {{AMC10 box|year=2008|ab=B|num-b=3|num-a=5}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Revision as of 23:53, 4 February 2017
Problem
A semipro baseball league has teams with 21 players each. League rules state that a player must be paid at least $15,000 and that the total of all players' salaries for each team cannot exceed $700,000. What is the maximum possible salary, in dollars, for a single player?
Solution
The maximum occurs when 20 players get the minimum wage and the total of all players' salaries is 700000. That is when one player gets 
.
See also
| 2008 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
