Each girl scored 9 points
Each boy scored 7 points
Explanation:
Let the number of points each girl scored = a
Let the number of points each boy scored = b
7 girls and 6 boys scored a total of 105 points.
7a + 6b = 105......... Equation 1
The difference between the number of points scored by the 7 girls and the number of points scored by the 6 boys is 21
7a - 6b = 21........... Equation 2
7a + 6b = 105......... Equation 1
7a - 6b = 21........... Equation 2
Subtract Equation 2 from Equation 1
12b = 84
b = 84/12
b = 7
Therefore, each boy scored 7 points
7a + 6b = 105......... Equation 1
b = 7
7a+ 6b = 105
7a + 6(7) = 105
7a + 42 = 105
7a = 105 - 42
7a = 63
a = 63/7
a = 9
Therefore, each girl scored 9 points.