Questions

To find the difference in winning percentages between the two sport teams after the next two games, we need to calculate the winning percentages for both teams before and after the two games.

1. Calculate the current winning percentage: Each team has won 5 games and lost 3 games. Thus, they each have played 8 games.

   Winning percentage $P$ is given by:

   $$P = \frac{\text{Number of Wins}}{\text{Total Number of Games}} \times 100$$

   For both teams currently:

   $$P = \frac{5}{8} \times 100 = 62.5\%$$

2. Determine the number of wins and losses after the next two games:

   • Team A wins the next two games, so their new record will be 7 wins and 3 losses.
   • Team B loses the next two games, so their new record will be 5 wins and 5 losses.

3. Calculate the new winning percentages:

   • For Team A:

     $$P_A = \frac{7}{7+3} \times 100 = \frac{7}{10} \times 100 = 70\%$$

   • For Team B:

     $$P_B = \frac{5}{5+5} \times 100 = \frac{5}{10} \times 100 = 50\%$$

4. Compute the difference in winning percentages:

   $$\text{Difference} = P_A - P_B = 70\% - 50\% = 20\%$$

The teams' winning percentages will differ by 20 percentage points after the next two games.