The night before their debut performance of Hamilton, the cast was staying at a hotel on Michigan Avenue. Fourteen members of the cast went to the casino to play poker. Half of the remaining cast went to the United Center to watch the Bulls play the Lakers. After about an hour, 6 of the cast members who had gone to play poker came back to the hotel, pockets empty. The 11 cast members now at the hotel went to bed and got enough sleep, but the rest of the cast were tired for their debut the next day. How many members are their in the cast?
x cast members at hotel
14 to casino
x-14 left at hotel
(x-14)/2 to UC, leaving (x-14)/2 at hotel
6 return to hotel, so
(x-14)/2 + 6 = 11
x = 24
The only problem with this is that 24-14 = 10, so only 5 could have gone to the UC. How could 6 have returned?
Have i missed something, or is there a typo somewhere?
Let's break down the information given step-by-step to determine the total number of members in the cast.
1. The night before the debut performance, the cast was staying at a hotel on Michigan Avenue.
2. Fourteen members of the cast went to the casino to play poker.
3. Half of the remaining cast went to the United Center to watch the Bulls play the Lakers.
4. After about an hour, 6 of the cast members who had gone to play poker came back to the hotel empty-handed.
5. The 11 remaining cast members at the hotel went to bed and got enough sleep.
6. The rest of the cast (those who went to the United Center) were tired for their debut the next day.
Let's calculate the total number of cast members in the following steps:
Step 1: Calculate the number of cast members who went to the casino to play poker.
14 members went to play poker.
Step 2: Calculate the number of cast members who went to watch the Bulls play the Lakers.
Half of the remaining cast went to the United Center.
Remaining cast members = Total cast members - Members who went to play poker
Remaining cast members = Total cast members - 14 members
Step 3: Calculate the number of cast members who returned from playing poker.
After about an hour, 6 members returned empty-handed.
Step 4: Calculate the number of cast members who were at the hotel, went to bed, and got enough sleep.
11 members were at the hotel and went to bed.
Step 5: Calculate the total number of cast members.
Total cast members = Members who went to play poker + Members who went to the United Center
Total cast members = 14 members + Remaining cast members
From the information given, we do not have a specific number for "Remaining cast members." Therefore, the number of members in the cast cannot be determined with the given information.
To find the number of cast members, let's break down the information given:
1. Initially, the entire cast was at the hotel.
2. 14 cast members went to play poker. This means we have 14 fewer cast members at the hotel.
3. The remaining cast members split in half, with half going to watch the Bulls play the Lakers. This means we have half of the original number of cast members at the hotel.
4. 6 cast members came back from playing poker, leaving 11 cast members at the hotel.
Let's calculate step-by-step:
1. Subtract the 14 cast members who went to play poker from the original number of cast members.
2. Divide the remaining cast members by 2 to account for the split to watch the basketball game.
3. Subtract the 6 cast members who came back from playing poker.
4. You'll be left with the 11 cast members who stayed at the hotel.
Let's calculate the number of cast members:
Original number of cast members = X
Step 1: X - 14
Step 2: (X - 14) ÷ 2
Step 3: (X - 14) ÷ 2 - 6 = 11
Simplifying the equation:
(X - 14) ÷ 2 - 6 = 11
(X - 14) ÷ 2 = 11 + 6
(X - 14) ÷ 2 = 17
(X - 14) = 2 x 17
X - 14 = 34
X = 34 + 14
X = 48
Therefore, there are 48 members in the cast.