Question

a college food court surveyed 674 students to see how many drink soda, how many drink milk, 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.)

(a) how many of the students drink exactly one of the three drinks?
students

(b) how many of the students drink milk?
students

(c) how many of the students drink both coffee and soda, but don’t drink milk?
students

Explanation:

Step1: Find students who drink exactly one drink

Add the numbers in the non - overlapping parts of each circle.
For soda only: \(66\), for milk only: \(147\), for coffee only: \(44\).
Sum: \(66 + 147+44\)
$$66 + 147+44=(66 + 44)+147=110 + 147 = 257$$

Step2: Find students who drink milk

Add all the numbers in the milk circle.
\(37+147 + 145+71\)
$$37+147 + 145+71=(37+147)+(145 + 71)=184+216=400$$

Step3: Find students who drink both coffee and soda but not milk

Look at the intersection of coffee and soda that does not overlap with milk. The number is \(51\).

Answer:

(a) \(257\) students
(b) \(400\) students
(c) \(51\) students