Question

in the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-point shots. in the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half. which expression represents the total number of points the player scored in the game?

\\(2x + 3x + 9\\)
\\(2x + 3 + 9\\)
\\(2x + 3x + 9x\\)
\\(2 + 3x + 9\\)

Explanation:

Define the variable for the unknown quantity

Using the Algebraic Modeling knowledge point
Let \(x\) represent the number of 2-point shots scored in the first half of the game.

Determine points scored in the first half

Using the Algebraic Modeling knowledge point

• Points from free throws: \(9\)
• Points from 2-point shots: \(2 \cdot x = 2x\)
• Total first-half points: \(2x + 9\)

Determine points scored in the second half

Using the Algebraic Modeling knowledge point

• Number of 3-point shots: \(x\) (the same as the number of 2-point shots in the first half)
• Total second-half points: \(3 \cdot x = 3x\)

Combine to find the total points

Using the Algebraic Modeling knowledge point

$$ \text{Total Points} = (2x + 9) + 3x = 2x + 3x + 9 $$

Answer:

• (A) \(2x + 3x + 9\) (Correct answer)
• (B) \(2x + 3 + 9\)
• (C) \(2x + 3x + 9x\)
• (D) \(2 + 3x + 9\)