Question

In a hotel, 45 members take tea, 24 take coffee, and 18 take milk. 15 take both tea and coffee, 12 take milk and both. None take coffee and milk both or all three. Find the number of members in the hotel.

a) 60
b) 72
c) 80
d) 90

Answer 1

To find the number of members in the hotel, we can use the principle of inclusion-exclusion. By adding the number of people who take each beverage individually and subtracting the number of people who take two or three of these beverages, we can find the total number of members. In this case, the number of members in the hotel is 60.

Step-by-step explanation:

To find the number of members in the hotel, we can use the principle of inclusion-exclusion. We add the number of people who take tea, coffee, and milk individually, and then subtract the number of people who take two or three of these beverages to avoid double-counting.

Number of people who take tea = 45

Number of people who take coffee = 24

Number of people who take milk = 18

Number of people who take tea and coffee = 15

Number of people who take tea and milk = 12

Number of people who take coffee and milk = 0 (given)

Number of people who take all three beverages = 0 (given)

Using the principle of inclusion-exclusion, we can calculate the number of people in the hotel:

Total number of members = Number of people who take tea + Number of people who take coffee + Number of people who take milk - Number of people who take tea and coffee - Number of people who take tea and milk - Number of people who take coffee and milk + Number of people who take all three beverages

Total number of members = 45 + 24 + 18 - 15 - 12 - 0 + 0 = 60

Therefore, the number of members in the hotel is 60.