Question

The members of the boosters organization at your high school bought new balls for the school. They spent $16.00 per basketball and $30.00 per football, spending a total of $580.00. They bought 4 more footballs than basketballs. How many of each type of ball did they buy?

A) 10 basketballs and 14 footballs
B) 15 basketballs and 19 footballs
C) 8 basketballs and 12 footballs
D) 6 basketballs and 10 footballs

Answer 1

By setting up an equation using the given costs for basketballs and footballs, and the total amount spent, we solved for the number of basketballs bought (10) and found the number of footballs to be 4 more than that (14). Thus, the boosters organization bought 10 basketballs and 14 footballs (option A).

Step-by-step explanation:

Let's define variables to represent the number of basketballs and footballs. If we let x be the number of basketballs, then we have x + 4 for the number of footballs because they bought 4 more footballs than basketballs. The total cost for the basketballs is $16.00 per basketball, multiplying this by x gives us the total cost for basketballs, which is 16x dollars. Similarly, for footballs, at $30.00 per football, the total cost is 30(x + 4) dollars.

Combining both expenses, we set up the equation:

16x + 30(x + 4) = 580

Let's solve the equation step by step:

1. Distribute 30 into (x + 4) to get:
   16x + 30x + 120 = 580
2. Combine like terms:
   46x + 120 = 580
3. Subtract 120 from both sides:
   46x = 460
4. Divide both sides by 46:
   x = 10

We find that x (the number of basketballs) is 10. The number of footballs would be x + 4, so:

10 + 4 = 14

Therefore, they bought 10 basketballs and 14 footballs, which matches option A: 10 basketballs and 14 footballs.