Answer:
481 students
Explanation:
To find out how many students ate at least one meal in the cafeteria, we can use the principle of inclusion-exclusion.
We are given the following information:
- 134 students ate breakfast.
- 179 students ate lunch.
- 272 students ate dinner.
- 62 students ate breakfast and lunch.
- 110 students ate breakfast and dinner.
- 94 students ate lunch and dinner.
- 54 students ate all three meals.
First, let's calculate the total number of students who ate each meal individually:
Total students who ate breakfast = 134
Total students who ate lunch = 179
Total students who ate dinner = 272
Now, let's calculate the total number of students who ate exactly two meals:
Students who ate both breakfast and lunch = 62
Students who ate both breakfast and dinner = 110
Students who ate both lunch and dinner = 94
Now, we need to subtract the students who ate exactly two meals from the total students who ate those meals. This is because we've counted them twice when calculating the total for each meal:
Total students who ate breakfast - Students who ate both breakfast and lunch - Students who ate both breakfast and dinner = 134 - 62 - 110
Total students who ate lunch - Students who ate both breakfast and lunch - Students who ate both lunch and dinner = 179 - 62 - 94
Total students who ate dinner - Students who ate both breakfast and dinner - Students who ate both lunch and dinner = 272 - 110 - 94
Now, let's calculate these values:
Total students who ate breakfast = 134
Total students who ate lunch = 179
Total students who ate dinner = 272
Total students who ate at least one meal = (Total students who ate breakfast) + (Total students who ate lunch) + (Total students who ate dinner) - (Total students who ate breakfast and lunch and dinner)
Total students who ate at least one meal = 134 + 179 + 272 - 54
Total students who ate at least one meal = 535 - 54
Total students who ate at least one meal = 481
So, 481 students ate at least one meal in the cafeteria.