A baseball manager bought 4 bats and 9 balls for $76.50. On another day, she bought 3 bats and a dozen balls at the same prices and paid $81.00. How much did she pay for each bat and each ball. Write a system of equations in order to solve this problem.

bat, $9.00; ball, $4.50

Step-by-step explanation:

Unit cost of bat (y) in terms of unit cost of ball (x) - 2 equations combined:

4y + 9x - 3y - 12x = $76.50 - $81.00

y = 3x - $4.50

Price of a ball (x) - 1st equation, substitute y:

4 (3x - $4.50) + 9x = $76.50

12x - $18.00 + 9x = $76.50

21x = $94.50

x = $4.50

Cost of a bat-2 equations combined:

= 3 ($4.50) - $4.50

= $13.50 - $4.50

= $9.00