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

(Solution)
(Solution)
Line 8: Line 8:
  
 
<math>700,000 = 20 * 15,000 + x</math>
 
<math>700,000 = 20 * 15,000 + x</math>
 +
 
<math>x = 400,000</math>
 
<math>x = 400,000</math>
  
 
The maximum any player could make is <math>400,000</math> dollars (answer choice C)
 
The maximum any player could make is <math>400,000</math> dollars (answer choice C)

Revision as of 22:55, 1 March 2008

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 (answer choice C)