Question

A bat and a ball together cost $1.10. The bat costs $1.00 more than the ball. How much does the ball cost?

Answer 1

Let's denote the cost of the ball as \( x \) dollars. According to the problem, the bat costs $1.00 more than the ball, so the cost of the bat would be \( x + 1.00 \) dollars.

The total cost of the bat and ball together is given as $1.10. We can set up the following equation:

\[
x + (x + 1.00) = 1.10
\]

This simplifies to:

\[
2x + 1.00 = 1.10
\]

Now, subtract \( 1.00 \) from both sides:

\[
2x = 0.10
\]

Next, divide both sides by 2:

\[
x = 0.05
\]

So, the cost of the ball is \( 0.05 \) dollars, which is 5 cents.

To find the cost of the bat, we can substitute \( x \) back into our expression for the bat:

\[
\text{Bat cost} = x + 1.00 = 0.05 + 1.00 = 1.05
\]

Now, checking the total:

\[
0.05 + 1.05 = 1.10
\]

Thus, the solution is consistent. Therefore, the cost of the ball is:

\[
\boxed{0.05} \text{ dollars } (5 \text{ cents})
\]