Answer: Let's use a Venn diagram to solve this problem.
First, we know that 612 students like football, 540 students like volleyball, and all students like at least one game. This means that there is some overlap between the two groups in the Venn diagram.
Let x be the number of students who like both games. Then, the number of students who like only football is 612 - x, and the number of students who like only volleyball is 540 - x.
Since all 900 students like at least one game, we can add up the number of students in each of these three groups and set the sum equal to 900:
(612 - x) + x + (540 - x) = 900
Simplifying the left side of the equation gives:
1152 - 2x = 900
Subtracting 1152 from both sides gives:
-2x = -252
Dividing both sides by -2 gives:
x = 126
Therefore, 126 students like both football and volleyball.
To find the number of students who like only football, we can substitute x = 126 into the expression 612 - x:
612 - 126 = 486
Therefore, 486 students like only football.
Explanation: