Question

On a​ team, 3 girls and 2 boys scored a total of 27 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 15. 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

We can start solving the problem by using algebra. Let x be the number of points scored by each girl, and y be the number of points scored by each boy. Then, based on the information given in the problem, we have the following equations:

x + y = 27 (the total number of points scored by the team)

3x - 2y = 15 (the difference between the number of points scored by the 3 girls and the 2 boys)

To solve for x and y, we can use the second equation to eliminate one of the variables. Multiplying both sides of the second equation by 2, we get:

6x - 4y = 30

Now we can substitute this into the first equation:

6x - 4y + y = 27

6x = 27 + 4y

x = (27 + 4y)/6

Now we can substitute this back into the second equation:

3((27 + 4y)/6) - 2y = 15

27 + 2y - 2y = 15

27 = 15

This is a contradiction, so the given information is insufficient to find the number of points scored by each girl and each boy.

Explanation: