We're currently making plans for the homecoming dance, which will be in the gym this year. We'll move the bleachers up and put tables in their place, which will leave the entire basketball court for a dance area. If people need at least 7.7 square feet per person to dance, how many people can fit on our 84'x50' basketball court?

To determine how many people can fit on the basketball court, given that each person needs at least 7.7 square feet to dance, we'll follow these steps:

1. **Find the area of the basketball court**:  
   The dimensions of the basketball court are 84 feet by 50 feet.  
   \[
   \text{Area of the court} = 84 \times 50 = 4200 \, \text{square feet}
   \]

2. **Divide the total area by the space required per person**:  
   Each person needs 7.7 square feet to dance, so we divide the total area by 7.7:
   \[
   \text{Number of people} = \frac{4200}{7.7} \approx 545.45
   \]

Since we can't have a fraction of a person, we round down to 545 people.

**Conclusion**:  
Approximately **545 people** can fit on the basketball court for the dance.

Would you like further details or clarifications?

Here are some related questions to think about:
1. What if people need more or less space per person?
2. How many tables could fit if each table requires 30 square feet?
3. How many more people could fit if we opened up part of the bleachers?
4. What if we used only half of the court for dancing?
5. What is the capacity if the gym has additional floor space besides the court?

**Tip**: Always consider safety regulations when estimating capacity for events like dances!

Find out how many people can fit on an 84'x50' basketball court for a dance, given that each person needs 7.7 square feet. This problem involves calculating the area and dividing it by the space needed per person. Perfect for students in Grades 6-8 learning about geometry and unit rates.

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