Math Problem Statement

Brandon is a high school basketball player. In a particular game, he made some two-point shots and some three-point shots. Brandon scored a total of 16 points and made twice as many three-point shots as two-point shots. Write a system of equations that could be used to determine the number of two-point shots Brandon made and the number of three-point shots he made. Define the variables that you use to write the system.

Solution

Let's solve the problem together.

The question asks to define variables and write a system of equations for the number of two-point and three-point shots Brandon made, based on the following details:

  • Brandon scored a total of 16 points.
  • He made twice as many three-point shots as two-point shots.

Step 1: Define the variables

Let:

  • xx be the number of two-point shots.
  • yy be the number of three-point shots.

Step 2: Write the system of equations

From the problem:

  1. Total points: Brandon scored 16 points. Each two-point shot gives 2 points, and each three-point shot gives 3 points. The equation for total points is: 2x+3y=162x + 3y = 16
  2. Twice as many three-point shots: Brandon made twice as many three-point shots as two-point shots. This relationship can be written as: y=2xy = 2x

Final System of Equations:

2x + 3y &= 16 \\ y &= 2x \end{aligned}$$ Would you like more details or explanations? Here are some related questions to expand on the concept: 1. How can this system of equations be solved using substitution or elimination? 2. What happens if Brandon made three times as many three-point shots as two-point shots? 3. How would the system change if the total points were different, say 20 points instead of 16? 4. How can you represent this problem graphically? 5. What other types of sports scoring systems can be modeled using linear equations? **Tip**: Always double-check the relationships between variables when defining equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
System of Equations

Formulas

2x + 3y = 16
y = 2x

Theorems

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Suitable Grade Level

Grades 8-10

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