In a recent year a baseball team paid six times as much to their ace pitcher as they paid to their shortstop. If they paid $56 million for the two salaries, what did they pay each player
What was the pitcher's salary? S
(millions of dollars)
What was the shortstop's salary?
(millions of dollars)

Step-by-step explanation:

The ratio of salaries can be written as ...

   short : pitcher = 1 : 6

Then the fraction of the total that the shortstop received is ...

  short : total = 1 : (1+6) = 1 : 7

The shortstop's salary was (1/7)×($56 million) = $8 million.

The pitcher's salary was 6 times that, so 6×($8 million) = $48 million.

The pitcher's salary was $48 million; the shortstop's, $8 million.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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