1. **Stating the problem:** We have a survey of 75 people with age and food preference data. We want to find how many people aged 25 or less like both spicy and sweet food. 2. **Given data:** - Total people: 75 - People older than 25: 50 - People 25 or younger: 75 - 50 = 25 - People who like spicy food: 27 - Among spicy food lovers, 7 are 25 or younger - People who like sweet food: 28 - Among sweet food lovers, 25 are older than 25 - People who like both spicy and sweet: 5 - People who like neither spicy nor sweet: 25 - Among those who like neither, 7 are older than 25 3. **Define variables:** Let $x$ = number of people 25 or younger who like both spicy and sweet. 4. **Analyze spicy food lovers:** - Total spicy lovers = 27 - Spicy lovers 25 or younger = 7 - Spicy lovers older than 25 = 27 - 7 = 20 5. **Analyze sweet food lovers:** - Total sweet lovers = 28 - Sweet lovers older than 25 = 25 - Sweet lovers 25 or younger = 28 - 25 = 3 6. **Analyze people who like neither spicy nor sweet:** - Total neither = 25 - Neither older than 25 = 7 - Neither 25 or younger = 25 - 7 = 18 7. **Calculate total people 25 or younger:** - Total 25 or younger = 25 - They are divided into three groups: spicy only, sweet only, both spicy and sweet, and neither. 8. **Calculate people 25 or younger who like spicy only:** - Spicy 25 or younger = 7 - Among them, $x$ like both spicy and sweet - So spicy only 25 or younger = $7 - x$ 9. **Calculate people 25 or younger who like sweet only:** - Sweet 25 or younger = 3 - Among them, $x$ like both spicy and sweet - So sweet only 25 or younger = $3 - x$ 10. **Sum of 25 or younger groups:** $$ (7 - x) + (3 - x) + x + 18 = 25 $$ Simplify: $$ 7 - x + 3 - x + x + 18 = 25 $$ $$ 28 - x = 25 $$ $$ x = 28 - 25 = 3 $$ 11. **Answer:** The number of people 25 or younger who like both spicy and sweet food is **3**. **Final answer: B. 3**