Question

Evie was doing a science fair project by surveying 30 students. 15 had brown hair and 17 had blue eyes and 6 had neither brown hair nor blue eyes. Determine the number of students who had brown hair and blue eyes.

Answer 1

The number of students who had brown hair and blue eyes = 8

Explanation:

It is given that,There are total 30 students.

15 had brown hair and 17 had blue eyes and 6 had neither brown hair nor blue eyes.

From the given information we get,

The number students in which either brown hair or blue eyes or both is given by = 30 - 6 = 24

Let x students had brown hair and y students had blue eyes

x∩y = the number of students who had brown hair and blue eyes

x = 15 and y = 17

we can write

24 = x + y - x∩y

x∩y = x + y -24 = 15 + 17 - 24

x∩y = 8

Therefore the number of students who had brown hair and blue eyes = 8

Answer 2

8 students

Explanation:

Let x be the number of students which had brown hair and blue eyes. Then

• 15-x students had only brown hair;
• 17-x students had only blue eyes;
• (15-x)+x+(17-x) students had brown hair or blue eyes.

Hence,

30-((15-x)+x+(17-x)) students had neither brown hair nor blue eyes.

`30-((15-x)+x+(17-x))=30-15+x-x-17+x=x-2=6,\\ \\x=8.`