1. In a class of students the ratio of the number of students who like to play football and the number of students who like to play volleyball is 5:3. If the number of students who like volleyball only is 15 and the number of students who like football only is 35, then a. Find the number of students who like both games. ​

Both sports = 15

Step-by-step explanation:

Remark

What an interesting question. At first I didn't think it was possible. Then I saw the word only. That made all the difference in the world.

Givens

Football only = 35

Volleyball only = 15

Ratio = 5/3

Equation

Let the number of students who play both = x

Volleyball / Football = (x + 15) /(x + 35) = 3/5

Solution

(x + 15) / (x + 35) = 3/5                  Cross multiply

5*(x + 15) = 3(x + 35)                     Remove the brackets

5x + 75 = 3x + 105                        Subtract 3x from both sides

3x            3x

2x + 75 = 105                               Subtract 75 from both sides

      - 75   -75  

2x = 30                                        Divide by 2  

2x/2 = 30/2

x = 15

15 people play both sports.

b, i believe, but not sure.