Question

Each football costs the same amount, and each basketball costs the same amount. At the first store, the coach paid $110 for 5 footballs and 14 basketballs. At the second store, the coach paid $82.50 for 10 footballs and 6 basketballs. What was the cost in dollars of each basketball?

Answer 1

$6.25

Explanation:

Each football costs the same amount, and each basketball costs the same amount.

Let the cost of:

Footballs = f

Basketballs = b

Hence, we have the following system of equations

At the first store, the coach paid $110 for 5 footballs and 14 basketballs.

5f + 14b = 110

At the second store, the coach paid $82.50 for 10 footballs and 6 basketballs.

10f + 6b = 82.50

What was the cost in dollars of each basketball?

5f + 14b = 110..... Equation 1

10f + 6b = 82.50.....Equation 2

We solve using Elimination method.

Multiply Equation 1 by 10 and Equation 2 by 5 to eliminate f

50f + 140b = 1100.... Equation 3

50f +30b = 412.5.......Equation 4

Subtract Equation 4 from Equation 3

110b = 687.5

b= 687.5/110

b = $6.25

Therefore, the cost of one basketball in dollars = $6.25