Seven subtracted from 4 times a number (x) is more than 13

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.