Question

a college food court surveyed 299 students to see how many drink coffee and how many drink soda.
the venn diagram below shows the results. (each number gives the number of students who fall into that venn diagram category.)
(a) how many of the students do not drink coffee?
students
(b) how many of the students drink coffee or soda (or both)?
students
(c) how many of the students drink coffee but do not drink soda?
students

Explanation:

Step1: Find students who do not drink coffee

Students who do not drink coffee are those in "Drink soda" only and outside both circles.
$$33 + 122=155$$

Step2: Find students who drink coffee or soda (or both)

Add all parts except the outside - only part.
$$41+103 + 33=177$$

Step3: Find students who drink coffee but not soda

This is the part of "Drink coffee" circle not overlapping with "Drink soda".
$$41$$

Answer:

(a) \(155\) students
(b) \(177\) students
(c) \(41\) students