Question

zane owns a restaurant, which features wings and ice cream. he is considering two new flavors of wings: parmesan garlic and mango habanero. zane tested the new flavors on 100 people and obtained the following results: 53 liked parmesan garlic; 38 liked both; 15 did not like either. use a venn diagram to complete parts (a) and (b). (a) how many people liked only mango habanero? 32 (type a whole number.) (b) how many people did not like mango habanero? (type a whole number.)

Explanation:

Step1: Find number of people who like at least one flavor

Total number of people is 100 and 15 did not like either. So number of people who like at least one flavor is $100 - 15=85$.

Step2: Find number of people who like only parmesan - garlic

Number of people who like parmesan - garlic is 53 and 38 like both. So number of people who like only parmesan - garlic is $53 - 38 = 15$.

Step3: Find number of people who like only mango habanero

Let number of people who like only mango habanero be $x$. We know that number of people who like at least one flavor is 85. So $x+38 + 15=85$. Solving for $x$, we get $x=85-(38 + 15)=32$.

Step4: Find number of people who did not like mango habanero

Number of people who like only parmesan - garlic is 15 and number of people who like neither is 15. So number of people who did not like mango habanero is $15+15 = 30$.

Answer:

(a) 32
(b) 30