Difference between revisions of "2008 AMC 12B Problems/Problem 3"

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<math>x = 400,000</math>
 
<math>x = 400,000</math>
  
The maximum any player could make is <math>400,000</math> dollars <math>\Rightarrow</math> C
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The maximum any player could make is <math>400,000</math> dollars <math>\Rightarrow C</math>
  
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2008|ab=B|num-b=2|num-a=4}}
 
{{AMC12 box|year=2008|ab=B|num-b=2|num-a=4}}

Revision as of 15:43, 21 February 2011

Problem 3

A semipro baseball league has teams with $21$ players each. League rules state that a player must be paid at least $15,000$ dollars, and that the total of all players' salaries for each team cannot exceed $700,000$ dollars. What is the maximum possiblle salary, in dollars, for a single player?

$\textbf{(A)}\ 270,000 \qquad \textbf{(B)}\ 385,000 \qquad \textbf{(C)}\ 400,000 \qquad \textbf{(D)}\ 430,000 \qquad \textbf{(E)}\ 700,000$

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 $700,000$

$700,000 = 20 * 15,000 + x$

$x = 400,000$

The maximum any player could make is $400,000$ dollars $\Rightarrow C$

See Also

2008 AMC 12B (ProblemsAnswer KeyResources)
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