Question

The tennis team has played 28 matches so far this season. They have won 10 matches so far. How many matches will the team need to win for the team to have a 55% success rate?

3
8
12
18

Answer 1

To find out how many matches the team needs to win to have a 55% success rate, we can set up the equation as follows:

Let \( x \) be the number of additional matches they need to win. The total number of matches played will then be \( 28 + x \), and the total number of wins will be \( 10 + x \).

We want the team's winning percentage to equal 55%, which can be expressed as:

\[
\frac{10 + x}{28 + x} = 0.55
\]

Now, we can solve for \( x \):

1. Multiply both sides by \( 28 + x \):

\[
10 + x = 0.55(28 + x)
\]

2. Distribute \( 0.55 \):

\[
10 + x = 15.4 + 0.55x
\]

3. Rearrange the equation by isolating \( x \) terms on one side:

\[
10 + x - 0.55x = 15.4
\]

This simplifies to:

\[
10 + 0.45x = 15.4
\]

4. Subtract 10 from both sides:

\[
0.45x = 5.4
\]

5. Divide both sides by 0.45:

\[
x = \frac{5.4}{0.45}
\]
\[
x = 12
\]

Thus, the team needs to win **12** additional matches to reach a 55% success rate. The correct answer is:

**12**