120 students were surveyed about their food preferences. 62 liked pizza,75 liked burgers and 48 liked tacos. 15 liked all three. 93 liked pizza or burgers, 96 liked burgers or tacos, and 88 liked pizza or tacos.
a) construct a venn diagram that will display the above info (just tell me whats between all the circles and in them) [i also know 15 is in the middle]
b) state the number of people that liked none of the foods.
To construct a Venn diagram from the given information, we will start by filling in the information that is given from the question.
Let's label the circles as follows:
- Circle A represents the set of people who like pizza.
- Circle B represents the set of people who like burgers.
- Circle C represents the set of people who like tacos.
Now, let's identify the information to be placed in the Venn diagram:
- The intersection of A, B, and C (the overlapping part) represents the 15 students who like all three foods.
- The region inside A but outside B and C represents the students who like only pizza (62 - 15 = 47).
- The region inside B but outside A and C represents the students who like only burgers (75 - 15 = 60).
- The region inside C but outside A and B represents the students who like only tacos (48 - 15 = 33).
- The number of students who like pizza or burgers (including those who like all three) is 93.
- The number of students who like burgers or tacos (including those who like all three) is 96.
- The number of students who like pizza or tacos (including those who like all three) is 88.
Given this information, the completed Venn diagram would look like this:
___
| |
A |___|
| |___
B |_____| |
| | |
C |___|___|
Now, let's determine the number of people who liked none of the foods. To find this value, we need to consider the total number of surveyed students and subtract the number of people who liked at least one food.
Total surveyed students = 120
Number of people who liked at least one food = (students who liked pizza or burgers) + (students who liked burgers or tacos) + (students who liked pizza or tacos) - (students who liked all three)
= 93 + 96 + 88 - 15
= 262 - 15
= 247
Therefore, the number of people who liked none of the foods is:
Number of people who liked none of the foods = Total surveyed students - Number of people who liked at least one food
= 120 - 247
= -127
Since we cannot have negative numbers of students, it seems that there is an error in the given information or in our calculations. Please double-check the information provided to ensure its accuracy.