Problem
3. Some people were asked if they like chocolate ice cream or strawberry ice cream. $70 \%$ said they like chocolate ice cream, $82 \%$ said they like strawberry ice cream, and $4 \%$ said they like neither. Answer part a and then complete each region of the Venn diagram. Use the diagram to answer parts b through e. a) How many percent like both chocolate ice cream AND strawberry ice cream? \[ 48 \% \] b) How many percent like both chocolate ice cream OR strawberry ice cream? c) How many percent like chocolate ice cream but not strawberry ice cream? d) How many percent like strawberry ice cream but not chocolate ice cream? e) How many percent do not like strawberry ice cream?
Solution
Step 1 ：The problem involves a survey where people were asked if they like chocolate ice cream or strawberry ice cream. From the survey, 70% said they like chocolate ice cream, 82% said they like strawberry ice cream, and 4% said they like neither.
Step 2 ：The total percentage of people who like either chocolate or strawberry or both is 100% - 4% = 96%.
Step 3 ：We know that 70% like chocolate and 82% like strawberry. The sum of these two percentages is 152%, which is greater than 96%.
Step 4 ：The difference, 152% - 96% = 56%, represents the people who like both chocolate and strawberry ice cream.
Step 5 ：Final Answer: The percentage of people who like both chocolate ice cream and strawberry ice cream is \(\boxed{56 \%}\).
