Answer:
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
<u>3x            3x</u>
2x + 75 = 105                               Subtract 75 from both sides
    <u>   - 75   -75  </u>
2x = 30                                        Divide by 2  
2x/2 = 30/2
x = 15
15 people play both sports.