Question 4
3 pts
At a high school, 82 students play video games during their free time, 115 students ride skateboards, and 40 students play video games and ride the skateboard. How many students engage in at least one of these activities in their free time? (Enter your answer in the box below).

Step 1 ：The problem is asking for the total number of students who either play video games, ride skateboards, or do both. This is a classic problem of set theory where we need to find the union of two sets.

Step 2 ：The formula to find the union of two sets is: \(n(A \cup B) = n(A) + n(B) - n(A \cap B)\), where \(n(A \cup B)\) is the number of elements in the union of sets A and B, \(n(A)\) is the number of elements in set A, \(n(B)\) is the number of elements in set B, and \(n(A \cap B)\) is the number of elements in both sets A and B.

Step 3 ：In this case, set A is the set of students who play video games, set B is the set of students who ride skateboards, and set \(A \cap B\) is the set of students who do both activities.

Step 4 ：We can substitute the given values into the formula to find the answer: \(n_A = 82\), \(n_B = 115\), \(n_{A \cap B} = 40\).

Step 5 ：Substituting these values into the formula, we get \(n_{A \cup B} = 82 + 115 - 40 = 157\).

Step 6 ：Final Answer: The number of students who engage in at least one of these activities in their free time is \(\boxed{157}\).