Question

a college food court surveyed 337 students to see how many drink tea and how many drink coffee.
the venn diagram below shows the results. (each number gives the number of students who fall into that venn diagram category.)
all students in the survey
(a) how many of the students do not drink coffee?
students
(b) how many of the students drink both tea and coffee?
students
(c) how many of the students drink tea or coffee (or both)?
students

Explanation:

Step1: Find students who do not drink coffee

Students who do not drink coffee are those only in the tea - only part and the part outside both circles.
$$119 + 73=192$$

Step2: Find students who drink both tea and coffee

The intersection of the two circles represents students who drink both.
$$68$$

Step3: Find students who drink tea or coffee (or both)

Sum up the values in the tea circle, coffee circle (subtracting the intersection once to avoid double - counting).
$$119+68 + 77=264$$

Answer:

(a) \(192\) students; (b) \(68\) students; (c) \(264\) students