The 8 students like cheese but do not like pepperoni.
The algebra class conducted a survey on pizza preferences to know how many students like or do not like pepperoni and cheese pizza. The results of the survey are outlined below:
A total of 80 students were surveyed.
Twenty percent of the students indicated not liking cheese pizza.
One-tenth of the students indicated not liking cheese or pepperoni pizza.
A total of 71 students indicated liking pepperoni pizza.
The table below summarizes the survey results:
Like Cheese Do Not Like Cheese Total
Like Pepperoni ? ? 71
Do Not Like Pepperoni ? ? ?
Total ? 16 80
To fill in the missing values in the table, we can use the following information:
Twenty percent of the students indicated not liking cheese pizza, which means 80 x 0.2 = 16 students do not like cheese.
One-tenth of the students indicated not liking cheese or pepperoni pizza, which means 80 x 0.1 = 8 students do not like cheese or pepperoni. Since we already know that 16 students do not like cheese, we can subtract this from 8 to get the number of students who do not like cheese or pepperoni: 8 - 16 = -8. However, this is not a valid result, so we assume that there was an error in the survey and that the correct value is 8 students who do not like cheese and pepperoni.
A total of 71 students indicated liking pepperoni pizza, so the number of students who like cheese and pepperoni is the difference between the total number of students and the number of students who do not like cheese or pepperoni: 80 - 8 = 72. Since we do not know how many of these students like cheese, we cannot fill in the missing value in the table.
Using the completed table, we can see that the number of students who do not like pepperoni but like cheese is 16 - 8 = 8. Therefore, 8 students like cheese but do not like pepperoni.