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?

Let \( x \) represent the number of 2-point shots, and \( y \) represent the number of 3-point shots. From the information given, we have two equations:

1. The total number of baskets is 20:
   \[
   x + y = 20
   \]
   
2. The total points scored is 48:
   \[
   2x + 3y = 48
   \]

### Step 1: Solve the first equation for \( y \)
From the first equation:
\[
y = 20 - x
\]

### Step 2: Substitute into the second equation
Substitute \( y = 20 - x \) into the second equation:
\[
2x + 3(20 - x) = 48
\]
Simplify:
\[
2x + 60 - 3x = 48
\]
\[
-x + 60 = 48
\]
\[
-x = 48 - 60
\]
\[
-x = -12
\]
\[
x = 12
\]

### Step 3: Solve for \( y \)
Now substitute \( x = 12 \) back into the equation \( y = 20 - x \):
\[
y = 20 - 12 = 8
\]

### Conclusion:
Angel made 12 two-point shots and 8 three-point shots. Therefore, the number of 2-point shots she made is:
\[
12 - 8 = 4
\]
So, Angel made 4 more 2-point shots than 3-point shots.

Do you want more details or have any questions?

Here are some related questions to practice:
1. What if Angel made 15 two-point shots and 5 three-point shots? How many total points would she have scored?
2. If Angel had scored 60 points with the same conditions, how would the number of 2-point and 3-point shots change?
3. How would the solution change if Angel made 25 baskets?
4. What would happen if Angel scored 48 points but could make only 3-point shots?
5. How many baskets would Angel need to score 48 points if all her baskets were 3-pointers?

**Tip:** When solving a system of equations, it’s often helpful to express one variable in terms of the other to simplify the substitution.

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?

Learn how to solve a real-world system of equations problem where Angel scores 48 points in a basketball game with 20 baskets, consisting of 2-point and 3-point shots. This step-by-step solution covers key algebraic concepts, including substitution, and is ideal for students in Grades 6-8.

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