Question

a movie club surveyed 100 high school students. the students were asked how often they go to the movies and whether they prefer action movies or comedies. their responses are summarized in the following table.

	action	comedy
three times a month or more	17	13

(a) what percentage of the students prefer action movies?
(b) what percentage of the students go to the movies three times a month or more?
(a) %
(b) %

Explanation:

Part (a)

Step1: Find total action movie lovers

To find the total number of students who prefer action movies, we add the number of students who watch action movies twice a month or less and three times a month or more. From the table, the number of students who watch action movies twice a month or less is 31, and three times a month or more is 17. So we calculate \(31 + 17\).
\(31+17 = 48\)

Step2: Calculate the percentage

The total number of students surveyed is 100. To find the percentage of students who prefer action movies, we use the formula \(\text{Percentage}=\frac{\text{Number of action movie lovers}}{\text{Total number of students}}\times100\%\). Substituting the values, we get \(\frac{48}{100}\times 100\%\).
\(\frac{48}{100}\times100\%= 48\%\)

Step1: Find total students who go three times or more

To find the total number of students who go to the movies three times a month or more, we add the number of students who prefer action movies and comedy movies and go three times a month or more. From the table, the number of action movie lovers who go three times a month or more is 17, and comedy movie lovers is 13. So we calculate \(17+13\).
\(17 + 13=30\)

Step2: Calculate the percentage

The total number of students surveyed is 100. To find the percentage, we use the formula \(\text{Percentage}=\frac{\text{Number of students who go three times or more}}{\text{Total number of students}}\times100\%\). Substituting the values, we get \(\frac{30}{100}\times100\%\).
\(\frac{30}{100}\times100\% = 30\%\)

Answer:

(a):
\(48\%\)

Part (b)