Questions: ARMY COLGATE 80.1 Points 67.4 29.7 Field Goals Made 25.4 65.7 Field Goals Attempted 57.8 45% Field Goal Percentage 43% 9.6 3 Point Field Goals Made 8.9 28.4 3 Point Field Goals Attempted 26.9 33% 3 Point Field Goal Percentage 33% 11.2 Free Throws Made 7.7 16.3 Free Throws Attempted 11 68% Free Throw Percentage 69% 35.3 Rebounds 27.8 10.2 Offensive Rebounds 6.4 25.1 Defensive Rebounds 21.4 17.3 Assists 13.5 10.8 Turnovers 10.8 6.5 Steals 6.5 2.3 Blocks 2 14.2 Personal Fouls 15.2

Solution Steps

To determine the possessions for each team, we use the formula:

\[ \text{Possessions} = \text{Field Goals Attempted} + 0.44 \times \text{Free Throws Attempted} - \text{Offensive Rebounds} + \text{Turnovers} \]

For Team A: \[ \text{Possessions}_A = 65.7 + 0.44 \times 16.3 - 10.2 + 10.8 = 73.472 \]

For Team B: \[ \text{Possessions}_B = 57.8 + 0.44 \times 11 - 6.4 + 10.8 = 67.04 \]

The offensive rating is calculated using the formula:

\[ \text{Offensive Rating} = \left( \frac{\text{Points}}{\text{Possessions}} \right) \times 100 \]

For Team A: \[ \text{Offensive Rating}_A = \left( \frac{80.1}{73.472} \right) \times 100 \approx 109.0211 \]

For Team B: \[ \text{Offensive Rating}_B = \left( \frac{67.4}{67.04} \right) \times 100 \approx 100.5370 \]

The defensive rating is calculated using the formula:

\[ \text{Defensive Rating} = \left( \frac{\text{Opponent Points}}{\text{Opponent Possessions}} \right) \times 100 \]

For Team A: \[ \text{Defensive Rating}_A = \left( \frac{67.4}{67.04} \right) \times 100 \approx 100.5370 \]

For Team B: \[ \text{Defensive Rating}_B = \left( \frac{80.1}{73.472} \right) \times 100 \approx 109.0211 \]

Final Answer