Explanation

Number of students who like football or hockey = Number of students who like football + Number of students who like hockey - Number of students who like both

We know that the total number of students is 49, and the number of students who like football or hockey is the sum of the students who like football and the students who like hockey, minus the students who like both (to avoid double-counting).

Let's denote the number of students who like both football and hockey as x.

Then, we can set up the equation:

49 = 35 + 29 - x

Combine like terms:

49 = 64 - x

Subtract 64 from both sides:

-15 = -x

Divide by -1:

x = 15

So, the number of students who like both football and hockey is 15.