Angel scored 48 points in her school's championship basketball game. She made 20 baskets with each basket being worth either 2 points or 3 points. How many more 2-point shots did A... Angel scored 48 points in her school's championship basketball game. She made 20 baskets with each basket being worth either 2 points or 3 points. How many more 2-point shots did Angel make than 3-point shots?
Understand the Problem
The question is asking how many more 2-point shots Angel made compared to 3-point shots, given her total points, number of baskets, and the point values of the baskets.
Answer
Angel made $4$ more 2-point shots than 3-point shots.
Answer for screen readers
Angel made 4 more 2-point shots than 3-point shots.
Steps to Solve
- Define the Variables
Let:
- $x$ = number of 2-point shots
- $y$ = number of 3-point shots
- Set Up the Equations
From the problem, we know:
- The total number of baskets: $$ x + y = 20 $$
- The total points scored: $$ 2x + 3y = 48 $$
- Express One Variable in Terms of Another
From the first equation, solve for $y$: $$ y = 20 - x $$
- Substitute into the Second Equation
Substitute $y$ into the second equation: $$ 2x + 3(20 - x) = 48 $$
- Simplify the Equation
Distributing the 3: $$ 2x + 60 - 3x = 48 $$
Combine like terms: $$ -x + 60 = 48 $$
- Solve for $x$
Subtract 60 from both sides: $$ -x = 48 - 60 $$ $$ -x = -12 $$ $$ x = 12 $$
- Find $y$
Using $y = 20 - x$: $$ y = 20 - 12 $$ $$ y = 8 $$
- Determine the Difference
Now, we find how many more 2-point shots than 3-point shots: $$ x - y = 12 - 8 = 4 $$
Angel made 4 more 2-point shots than 3-point shots.
More Information
In basketball, understanding shot value can be crucial for strategy. The problem also demonstrates how to work with systems of equations, a foundational math concept.
Tips
- Forgetting to set up both equations correctly.
- Mixing up the values when substituting in equations.
- Not checking if the final numbers make sense in context.
