Question
At a high school, 84 students play video games during their free time, 129 students ride
skateboards, and 43 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).
skateboards, and 43 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).
Ask by Weston Vargas. in the United States
Mar 29,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
170 students engage in at least one of these activities in their free time.
Solution
Step 1: Identify the number of students who play video games, ride skateboards, and do both.
Step 2: Use the inclusion-exclusion principle to find the total number of students engaged in at least one activity:
Step 3: Substitute the given numbers into the formula:
Step 4: Perform the calculations:
Final Answer:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To find the number of students who engage in at least one of these activities, we can use the principle of inclusion-exclusion.
We have:
- Students who play video games (A) = 84
- Students who ride skateboards (B) = 129
- Students who both play video games and ride skateboards (A ∩ B) = 43
Using the formula:
|A ∪ B| = |A| + |B| - |A ∩ B|
|A ∪ B| = |A| + |B| - |A ∩ B|
Substituting the values:
|A ∪ B| = 84 + 129 - 43 = 170
|A ∪ B| = 84 + 129 - 43 = 170
So, 170 students engage in at least one of these activities.
