Question

A baseball coach bought 4 bats and 7 balls for $68. The next day the coach bought 1 bat and 1 ball for $14.

How much does each bat and ball cost based on the given information?
A. Each bat costs $6, and each ball costs $4.
B. Each bat costs $12, and each ball costs $6.
C. Each bat costs $7, and each ball costs $5.
D. Each bat costs $8, and each ball costs $7.

Answer 1

To solve for the cost of a bat and a ball, we form two equations based on the provided information and solve for the two variables. After setting up the equations, we use the substitution method to find that each bat costs $10, and each ball costs $4.

Step-by-step explanation:

Calculating the Cost of Each Bat and Ball

Given two systems of equations based on the information provided:

1. 4 bats + 7 balls = $68
2. 1 bat + 1 ball = $14

We can represent the cost of a bat by b and the cost of a ball by ball. Therefore, we have:

1. 4b + 7ball = 68
2. b + ball = 14

From equation (2), we can find the expression for b:
b = 14 - ball

Substituting the value of b into equation (1), we get:
4(14 - ball) + 7ball = 68
56 - 4ball + 7ball = 68
3ball = 12
ball = 4

Since we now know the cost of a ball, we can substitute back into equation (2) to find the cost of a bat:
b = 14 - 4
b = 10

Thus, each bat costs $10 and each ball costs $4.