To predict the number of losses for next year based on the provided historical data, we will follow these steps:
1. Identify and List the Wins and Losses:
- Year 1: 18 wins and 2 losses
- Year 2: 45 wins and 5 losses
- Year 3: 36 wins and 4 losses
- Next year (Predicted): 27 wins and \( x \) losses
2. Calculate the Win-to-Loss Ratio for Each Year:
- Year 1: \( \frac{18}{2} = 9 \)
- Year 2: \( \frac{45}{5} = 9 \)
- Year 3: \( \frac{36}{4} = 9 \)
3. Determine the Average Win-to-Loss Ratio:
- Each year has a win-to-loss ratio of \( 9 \)
- The average ratio is thus \( 9 \)
4. Use the Average Ratio for Prediction:
- Given that the team's performance is consistent, we assume the same ratio for the upcoming year.
- Therefore, with 27 wins predicted next year, the ratio \( 9 \) should be used to find the expected number of losses.
5. Set Up the Proportion and Solve for \( x \):
- Ratio: \( \frac{\text{wins}}{\text{losses}} = 9 \)
- For 27 wins: \( \frac{27}{x} = 9 \)
6. Solve the Equation for \( x \):
[tex]\[
\frac{27}{x} = 9
\][/tex]
Multiply both sides by \( x \) to isolate \( 27 \) on the left side:
[tex]\[
27 = 9x
\][/tex]
Divide both sides by \( 9 \) to solve for \( x \):
[tex]\[
x = \frac{27}{9} = 3
\][/tex]
Therefore, Will should predict 3 losses for the next year if the number of games won is 27. Thus, the correct answer is:
[tex]\[ \boxed{3} \][/tex]
