Answer: 76 baseballs and 24 bats were ordered.
Explanation:
Let x represent the number of baseballs that were ordered for the summer basketball camp.
Let y represent the number of bats that were ordered for the summer basketball camp.
Bakersfield parks and recreation department ordered a total of 100 baseballs and bats for the summer basketball camp. This means that
x + y = 100
Baseballs cost $4.50 each and bats cost $20 each. The total purchase was $822. This means that
4.5x + 20y = 822 - - - - - - - - - - -1
Substituting x = 100 - y into equation 1, it becomes
4.5(100 - y) + 20y = 822
450 - 4.5y + 20y = 822
- 4.5y + 20y = 822 - 450
15.5y = 372
y = 372/15.5
y = 24
x = 100 - y = 100 - 24
x = 76