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 \( x \):
- Multiply both sides by \( 28 + x \):
\[ 10 + x = 0.55(28 + x) \]
- Distribute \( 0.55 \):
\[ 10 + x = 15.4 + 0.55x \]
- Rearrange the equation by isolating \( x \) terms on one side:
\[ 10 + x - 0.55x = 15.4 \]
This simplifies to:
\[ 10 + 0.45x = 15.4 \]
- Subtract 10 from both sides:
\[ 0.45x = 5.4 \]
- 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