Before school began, Mrs. Weeks bought a total of 86 balls. Use the information below to help you write a numerical expression for the number of each type of ball. Then record the total number of each type of ball.

Question

Footballs- there are 8 footballs.
Basketballs- Two more than twice the number of footballs are basketballs
Baseballs- Four less than 5 times the number of footballs are baseballs.
Softballs- Six more than half of the baseballs are softballs.

Type of Ball Numerical expression for the number of Balls Total number
Football (given) 8
Basketball
Baseball
Softball
Use the space below to show your work
Directions: use the information you found in Part 1 to help you answer Part 2.
Cost per ball football basketball baseball softball
$8.00 $9.00 $7.00 $5.00

1. When Mrs. Weeks bought all of the baseballs and softballs, she paid for them using four $100.00 bills. How much change did dhe receive?
2. Write expressions that include parentheses and order of operations to show to find the answer. Show your work.
3.After school began, Mrs. Weeks realized that she needed more basketballs and footballs. If she spent $135.00 on basketballs and $48.00 on footballs, how many more balls did she purchase?
4. Write expressions the include parentheses and order of operations to show how to find the answer. Show your work.

Answer 1

1.
Baseballs: 4 less than 5 times the number of footballs = 5(8) - 4 = 40 - 4 = 36
Softballs: 6 more than half of the baseballs = (36 / 2) + 6 = 18 + 6 = 24

Total number of baseballs and softballs = 36 + 24 = 60

Cost of baseballs and softballs = 60 x $7.00 = $420.00
Change received = $400.00 - $420.00 = $20.00

2.
To find the sum of the cost of baseballs and softballs:
(5 x 8 - 4) x $7.00 + (6 + (5 x 8 - 4) / 2) x $5.00 = $420.00
To find the change:
$400.00 - ((5 x 8 - 4) x $7.00 + (6 + (5 x 8 - 4) / 2) x $5.00) = $20.00

3.
Total cost of basketballs = $135.00
Cost per basketball = $9.00
Number of basketballs purchased = 135 / 9 = 15

Total cost of footballs = $48.00
Cost per football = $8.00
Number of footballs purchased = 48 / 8 = 6

Total number of basketballs and footballs purchased = 15 + 6 = 21

4.
To find the number of basketballs purchased:
$135.00 / $9.00 = 15
To find the number of footballs purchased:
$48.00 / $8.00 = 6
Total number of balls purchased:
$135.00 / $9.00 + $48.00 / $8.00 = 15 + 6 = 21