Question

On a​ team, 3 girls and 2 boys scored a total of 23 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 7. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy.

Answer 1

Let \( g \) be the number of points scored by each girl and \( b \) be the number of points scored by each boy.

From the problem, we can set up the following equations based on the information given:

1. The total points scored by the girls and boys:
\[
3g + 2b = 23
\]

2. The difference between the points scored by the girls and boys:
\[
3g - 2b = 7
\]

We can solve these two equations simultaneously.

**Step 1: Solve for one variable**

Let's first solve the second equation for \( 3g \):
\[
3g = 2b + 7
\]

**Step 2: Substitute into the first equation**

Now, we substitute \( 3g \) in the first equation:
\[
(2b + 7) + 2b = 23
\]

Combine the terms to simplify:
\[
4b + 7 = 23
\]

**Step 3: Solve for \( b \)**

Subtract 7 from both sides:
\[
4b = 16
\]

Now, divide by 4:
\[
b = 4
\]

**Step 4: Substitute back to find \( g \)**

Now that we have \( b \), we can substitute it back into the equation for \( 3g \):
\[
3g = 2(4) + 7 = 8 + 7 = 15
\]

Now, divide by 3 to find \( g \):
\[
g = 5
\]

**Final Answer:**
Each girl scored \( 5 \) points, and each boy scored \( 4 \) points.

Thus, the results are:
- Points scored by each girl: \( \boxed{5} \)
- Points scored by each boy: \( \boxed{4} \)