SOLUTION: A tourist town has 1621 visitors this year. 70% of them have breakfast in a cafe and then 72% have lunches, 66% - dinner(all percentages are of the total visitors). There are 3 caf

Algebra ->  Probability-and-statistics -> SOLUTION: A tourist town has 1621 visitors this year. 70% of them have breakfast in a cafe and then 72% have lunches, 66% - dinner(all percentages are of the total visitors). There are 3 caf      Log On


   

Question 1192673: A tourist town has 1621 visitors this year. 70% of them have breakfast in a cafe and then 72% have lunches, 66% - dinner(all percentages are of the total visitors). There are 3 cafes in town and a local man wants to establish a new one. How many seats should the new cafe have so that it would be fully seated no less than 24% of dinner servings? What percentage of times would this new cafe be fully seated during breakfast and lunch servings?
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
**1. Calculate the number of visitors for each meal:**
* **Breakfast:** 1621 visitors * 70% = 1134.7 visitors ≈ 1135 visitors
* **Lunch:** 1621 visitors * 72% = 1163.52 visitors ≈ 1164 visitors
* **Dinner:** 1621 visitors * 66% = 1069.86 visitors ≈ 1070 visitors
**2. Determine the required seating for dinner:**
* Target dinner occupancy: 24% of dinner visitors
* Required dinner servings: 1070 visitors * 24% = 256.8 servings ≈ 257 servings
**3. Calculate the number of seats for the new cafe:**
* The new cafe needs at least 257 seats to accommodate 24% of dinner servings.
**4. Calculate the percentage of times the new cafe would be fully seated during breakfast and lunch:**
* **Assumption:** We assume that visitors are evenly distributed among the 4 cafes (including the new one).
* **Breakfast:**
* Total breakfast capacity: 257 seats/cafe * 4 cafes = 1028 seats
* Percentage full: 1135 visitors / 1028 seats = 1.10 ≈ 110% (This means the cafes would be overbooked during breakfast)
* **Lunch:**
* Total lunch capacity: 1028 seats
* Percentage full: 1164 visitors / 1028 seats = 1.13 ≈ 113% (Also overbooked during lunch)
**Therefore:**
* The new cafe should have at least **257 seats**.
* The cafes would likely be **overbooked** during both breakfast and lunch, assuming even distribution of visitors.
**Note:** This analysis assumes that all visitors who have breakfast, lunch, or dinner will choose to eat at a cafe. In reality, some visitors might eat elsewhere (e.g., restaurants, hotels).