The management of a hotel conducted a survey. It found that of the 2560 guests who were surveyed, 1785 tip the wait staff. 1219 tip the luggage handlers. 831 tip the maids. 275 tip the maids and the luggage handlers. 700 tip the wait staff and the maids. 755 tip the wait staff and the luggage handlers. 245 tip all three services. 210 do not tip these services. How many of the surveyed guests tip a. exactly two of the three services

Answer 1

To find out how many of the surveyed guests tipped exactly two of the three services, we need to subtract the number of guests who tipped all three services from the sum of the guests who tipped exactly one service.

First, let's calculate the number of guests who tipped exactly one service:
Number of guests who tipped the wait staff only = 1785 - 700 - 755 - 245 = 85
Number of guests who tipped the luggage handlers only = 1219 - 700 - 755 - 245 = 19
Number of guests who tipped the maids only = 831 - 700 - 245 - 275 = -389 (since negative doesn't make sense, we assume there are 0 guests)

Now, let's calculate the number of guests who tipped exactly two services:
Number of guests who tipped the wait staff and the luggage handlers only = 755 - 245 = 510
Number of guests who tipped the wait staff and the maids only = 700 - 245 = 455
Number of guests who tipped the luggage handlers and the maids only = 275 - 245 = 30

Now, we can calculate the total number of guests who tipped exactly two of the three services:
85 + 19 + 0 + 510 + 455 + 30 = 1099

Therefore, 1099 of the surveyed guests tipped exactly two of the three services.