Question

If a baseball and bat cost $110, and the bat costs $100 more than the ball, how much does the ball cost?

Answer 1

We can calculate this using a couple of equations. First, we need to define the two algebraically. We'll use A for the bat, and B for the ball.

We know that both of these together cost $110. Therefore, A + B = 110.

We also know that the bat costs $100 more than the ball. Therefore, A = B + 100.

This is now our system of equations.

A + B = 110
A = B + 100.

Because we know the value of A as it relates to B, we can solve by substitution. We replace A with B + 100 to get our new equation.

B + 100 + B = 110.

Collect like terms:

2B + 100 = 110

Take away 100 from both sides:

2B = 10

Divide by two:

B = 5.

So now we know that the ball is worth 5 dollars. What about the bat? There are two ways we could do this. The first is that A + B = 110.

A + 5 = 110.
A = 105.

The second way we can do this is that we know that the bat is worth 100 more than the ball.

A = 100 + 5.
A = 105.

Both solutions come up the same: The bat is worth 105, and the ball is worth 5.