Final answer:
By setting up a proportion of 7 wins in 11 games to x wins in 82 games and solving for x, we predict that the Spurs will win approximately 52 games in the 82-game season.
Step-by-step explanation:
The student's question involves using a proportion to predict the number of wins for the Spurs throughout an 82-game season based on their initial record of 7 wins and 4 losses. This can be set up as follows:
- Current win proportion: 7 wins out of 11 games, or \(\frac{7}{11}\).
- Desired win proportion: \(x\) wins out of 82 games, or \(\frac{x}{82}\).
To predict the total number of wins \(x\), we set up the proportion as \(\frac{7}{11} = \frac{x}{82}\) and solve for \(x\). Multiplying both sides by 82 gives us \(7 \times 82 = 11 \times x\). Simplifying, we get \(574 = 11x\). To find \(x\), we divide both sides of the equation by 11, which results in \(x = \frac{574}{11} = 52.1818\). Rounding to the nearest whole number, we can predict the Spurs will win approximately 52 games during the season.