You attend a party at your friend’s house and notice that about 1/3 of the main room is a slightly raised platform. You count that 24 people can fit comfortably on the platform. With this information, what is the best estimate for how many total people could fit comfortably in the main room? 





To estimate the total number of people who could fit comfortably in the main room, we can use the information that \( \frac{1}{3} \) of the room is occupied by the platform, which holds 24 people.

### Step 1: Determine the total capacity of the room
Since the platform represents \( \frac{1}{3} \) of the main room and 24 people fit on it, we can estimate the total capacity by multiplying this number by 3 (since \( \frac{1}{3} \) of the room corresponds to 24 people).

\[
\text{Total number of people} = 24 \times 3 = 72
\]

### Final Answer:
The best estimate for how many total people could fit comfortably in the main room is **72 people**.

Would you like more details or have any questions about this problem? Here are some additional related questions:

1. How would the estimate change if the platform occupied \( \frac{1}{4} \) of the room?
2. What assumptions are we making in this estimate?
3. If the room's capacity was 100 people, how many people would fit on the platform?
4. How would the estimate change if you found out that half the room was actually a platform?
5. How can this method of estimation be applied to other areas, like estimating the capacity of a bus or a theater?

**Tip:** Estimation is a valuable skill that helps in making quick decisions without needing precise calculations. It often involves proportional reasoning, as seen in this example.

Learn how to estimate the total capacity of a room using proportional reasoning. This problem involves determining the number of people that can fit in a main room based on a platform occupying one-third of the space. Explore the method used and its applications in various scenarios.

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