On a​ team, 7 girls and 5 boys scored a total of 103 points. The difference between the number of points scored by the 7 girls and the number of points scored by the 5 boys is 23. 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 the number of points scored by each girl be \( g \), and let the number of points scored by each boy be \( b \).

According to the problem, we have the following equations:

1. The total points scored by the girls and boys: \[ 7g + 5b = 103 \]

2. The difference in points scored: \[ 7g - 5b = 23 \]

We can solve these two equations simultaneously. First, let's solve for \( 7g \) in the second equation:

\[ 7g = 5b + 23 \]

Now we can substitute this expression for \( 7g \) into the first equation:

\[ (5b + 23) + 5b = 103 \]

Simplifying this gives:

\[ 10b + 23 = 103 \] \[ 10b = 103 - 23 \] \[ 10b = 80 \] \[ b = 8 \]

Now that we have \( b \), we can substitute it back into the equation for \( 7g \):

\[ 7g = 5(8) + 23 \] \[ 7g = 40 + 23 \] \[ 7g = 63 \] \[ g = \frac{63}{7} = 9 \]

Thus, each girl scored \( 9 \) points, and each boy scored \( 8 \) points.

To summarize:

• Each girl scored \( \boxed{9} \) points.
• Each boy scored \( \boxed{8} \) points.