In a recent game, a college basketball player made some baskets worth 2 points and some baskets worth 3 points. The basketball player scored 49 points in the game by making 20 bask... In a recent game, a college basketball player made some baskets worth 2 points and some baskets worth 3 points. The basketball player scored 49 points in the game by making 20 baskets. How many baskets worth 2 points did he make?
Understand the Problem
The question is asking how many baskets worth 2 points the basketball player made, given that he scored a total of 49 points by making 20 baskets, some worth 2 points and others worth 3 points. To solve this, we need to set up a system of equations based on the given conditions.
Answer
The basketball player made $11$ baskets worth 2 points.
Answer for screen readers
The basketball player made $11$ baskets worth 2 points.
Steps to Solve
-
Define Variables
Let $x$ be the number of baskets worth 2 points, and $y$ be the number of baskets worth 3 points. -
Set Up the Equations
From the problem, we have two equations:- The total number of baskets:
$$ x + y = 20 $$ - The total points scored:
$$ 2x + 3y = 49 $$
- The total number of baskets:
-
Solve the First Equation for One Variable
Let's solve for $y$ in terms of $x$:
$$ y = 20 - x $$ -
Substitute into the Second Equation
Substituting $y$ into the second equation:
$$ 2x + 3(20 - x) = 49 $$ -
Simplify the Equation
Distribute $3$ into the equation:
$$ 2x + 60 - 3x = 49 $$
Combine like terms:
$$ -x + 60 = 49 $$
-
Isolate x
Solve for $x$:
$$ -x = 49 - 60 $$
$$ -x = -11 $$
$$ x = 11 $$ -
Find y
Using the value of $x$ to find $y$:
$$ y = 20 - 11 = 9 $$
The basketball player made $11$ baskets worth 2 points.
More Information
In this problem, we set up a system of linear equations based on the constraints given (total baskets and total points) and solved for the number of baskets of each type.
Tips
- Forgetting to substitute correctly: When substituting one equation into another, ensure all terms are carried over correctly.
- Sign errors: Pay close attention to positive and negative signs, especially when isolating variables.
AI-generated content may contain errors. Please verify critical information
