Subjects algebra

Revenue Only Drinks E888C7

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1. **Problem statement:** Calculate the revenue from only drinks given the total revenue and percentages of revenue from entries, drinks, and food, including their intersections. 2. **Given data:** - Total revenue $= 200000$ - $P(E) = 53\%$ - $P(B) = 58\%$ - $P(C) = 17\%$ - $P(E \cap B) = 13\%$ - $P(E \cap C) = 10\%$ - $P(E \cap B \cap C) = 5\%$ - $P(\text{only } C) = 2\%$ 3. **Goal:** Find $P(\text{only } B)$, the revenue percentage from only drinks. 4. **Formula and rules:** Use the principle of inclusion-exclusion for three sets: $$ P(E \cup B \cup C) = P(E) + P(B) + P(C) - P(E \cap B) - P(E \cap C) - P(B \cap C) + P(E \cap B \cap C) $$ We know $P(\text{only } C) = P(C) - P(E \cap C) - P(B \cap C) + P(E \cap B \cap C) = 2\%$. 5. **Find $P(B \cap C)$:** $$ P(\text{only } C) = P(C) - P(E \cap C) - P(B \cap C) + P(E \cap B \cap C) \\ 2 = 17 - 10 - P(B \cap C) + 5 \\ 2 = 12 - P(B \cap C) \\ P(B \cap C) = 10\% $$ 6. **Calculate $P(\text{only } B)$:** $$ P(\text{only } B) = P(B) - P(E \cap B) - P(B \cap C) + P(E \cap B \cap C) \\ = 58 - 13 - 10 + 5 = 40\% $$ 7. **Calculate revenue from only drinks:** $$ \text{Revenue only drinks} = 40\% \times 200000 = 0.40 \times 200000 = 80000 $$ **Final answer:** The revenue from only drinks is 80000.