The Problem
There are 30 students in a class. Eleven have
blue eyes. Fifteen have brown hair. Three students have both blue
eyes and brown hair. How many students have neither blue eyes
nor brown hair?
(Source: Jon Basden) Submit your idea for an investigation
to InterMath
The Solution
This problem can be solved by thinking of members of the class
as belonging to four different categories: blue eyes, brown hair,
blue eyes and brown hair, or neither. We know that there are 11
students that have blue eyes and fifteen with brown hair, and
three with both. Since we know that 3 students have both blue
eyes and brown hair, we can subtract 3 from eleven and fifteen
to determine how many students have only blue eyes and how many
have only brown hair, then we can use those numbers to find out
how many students have neither blue eyes or brown hair.
11-3=8 students have only blue eyes
15-3=12 students have only brown hair
3 students have blue eyes and brown hair
Since there are 30 students in the class we can subtract the
above numbers to find out how many students have neither blue
eyes nor brown hair.
30-(8+12+3)= 30-23=7 students have neither