Question

On a​ team, 8 girls and 6 boys scored a total of 64 points. The difference between the number of points scored by the 8 girls and the number of points scored by the 6 boys is 16. 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.

a. Girls: 6 points, Boys: 4 points
b. Girls: 7 points, Boys: 5 points
c. Girls: 5 points, Boys: 3 points
d. Girls: 8 points, Boys: 6 points

Answer 1

By setting up equations based on the total points and the difference in points scored by girls and boys, we find that each girl scored 5 points, and each boy scored 4 points. The correct answer is option c.

Step-by-step explanation:

To solve this problem, let us denote the number of points that each girl scored as G and the number of points that each boy scored as B. It is given that:

• 8 girls and 6 boys scored a total of 64 points.
• The difference in points between the girls and boys is 16 points.

These two statements give us two equations:

1. 8G + 6B = 64 (Total points scored)
2. 8G - 6B = 16 (Difference in points)

By adding these two equations, we can eliminate B and solve for G:

1. 16G = 80
2. G = 5 (Each girl scored 5 points)

Now plug the value of G in one of the original equations to solve for B:

1. 8(5) + 6B = 64
2. 40 + 6B = 64
3. 6B = 24
4. B = 4 (Each boy scored 4 points)

Finally, the number of points scored by each girl is 5 and each boy is 4. Therefore, the correct option is c. Girls: 5 points, Boys: 3 points.