Question

Please Help!! Will reward best answer!
To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and the following data were obtained.

135 students ate breakfast
183 students ate lunch
278 students ate dinner
61 students ate breakfast and lunch
112 students ate breakfast and dinner
86 students ate lunch and dinner
52 students ate all three meals.

How many students ate:
(a) at least one meal in the cafeteria
(b) exactly one meal in the cafeteria
(c) only dinner in the cafeteria
(d) exactly two meals in the cafeteria

Answer 1

use a Venn diagram to help you.
When (almost) all the numbers are supplied, start with the middle (all three meals), then fill the ones with two meals, and calculate those with only one meal.
Use B=breakfast, L=lunch, D=dinner.
I'll give you a headstart:

When you complete the diagram, you can answer the given questions.

Answer 2

Ok, that helped alot, thank you! I completed my diagram and was able to answer almost all of the questions, but i am getting confused at the at least one meal vs exactly one meal.

Here is my diagram:

From there - 234

-234 students ate exactly one meal
-132 students ate only dinner int he cafeteria
-103 students ate exactly two meals in the cafeteria

I'm not sure hw to calculate at least one meal. How is that any different from the 234 tst students who ate ea exactly one meal?

Answer 3

Nevermind - i believe i figured it out. The answer for at least one meal is to add everything together. thank you for your help starting the diagram!

Answer 4

You're welcome! :)