Question

A survey asked 240 people if they liked a movie. One third liked it, one sixth did not like it, and one half had not see it. How many people are in each off the three categories?

Answer 1

The answer is that there are 80 people who liked the movie, 40 people who did not like it, and 120 people who had not seen it.

Explanation:

Let's denote the total number of people who liked the movie as \( L \), the total number of people who did not like it as \( D \), and the total number of people who had not seen it as \( N \).

The survey results are given as:

1. One-third liked the movie: \( L = \frac{1}{3} \times 240 \)

2. One-sixth did not like it: \( D = \frac{1}{6} \times 240 \)

3. One-half had not seen it: \( N = \frac{1}{2} \times 240 \)

Now, let's calculate these values:

1. \( L = \frac{1}{3} \times 240 = 80 \)

2. \( D = \frac{1}{6} \times 240 = 40 \)

3. \( N = \frac{1}{2} \times 240 = 120 \)

Therefore, there are 80 people who liked the movie, 40 people who did not like it, and 120 people who had not seen it.