Research results for a concert show that 10,000 people will attend the concert if the price is $20 per tickets. For each dollar increase in price, 1000 fewer people will attend. 

This problem presents a linear relationship between the ticket price and the number of attendees. Let’s define the variables first:

- Let $ p $ represent the price of the ticket.
- Let $ n(p) $ represent the number of attendees when the ticket price is $ p $.

### Step-by-step breakdown:

1. **Given conditions:**
   - When the price is $20, 10,000 people will attend, so:
     \[
     n(20) = 10,000
     \]
   - For each dollar increase in price, 1,000 fewer people will attend.

2. **Building the equation:**
   - We know that for every $1 increase in price, the attendance decreases by 1,000 people. This implies a negative slope for the linear relationship between price and attendance.
   - Let the slope of the linear equation be $-1,000$ (since for every increase in price by 1 dollar, 1,000 fewer people will attend).
   
   The general form of the linear equation is:
   \[
   n(p) = 10,000 - 1,000(p - 20)
   \]
   where $ p - 20 $ represents the increase in price above $20.

3. **Simplifying the equation:**
   \[
   n(p) = 10,000 - 1,000(p - 20)
   \]
   \[
   n(p) = 10,000 - 1,000p + 20,000
   \]
   \[
   n(p) = 30,000 - 1,000p
   \]

Thus, the number of attendees $ n(p) $ as a function of the ticket price $ p $ is:
\[
n(p) = 30,000 - 1,000p
\]

### Interpretation:
- The equation $ n(p) = 30,000 - 1,000p $ tells us that for each dollar increase in price, the attendance will decrease by 1,000 people. At a ticket price of $20, there will be 10,000 attendees, and as the price increases, attendance decreases linearly.

Would you like to dive into more details or solve related questions?

### Related Questions:
1. What price will result in no one attending the concert?
2. How does the revenue change as the ticket price increases?
3. What ticket price will maximize the revenue?
4. What is the revenue when the ticket price is $25?
5. How many people will attend if the ticket price is $15?

### Tip:
Always check if a linear relationship can be simplified to find clearer patterns in word problems.

Research results for a concert show that 10,000 people will attend the concert if the price is $20 per ticket. For each dollar increase in price, 1,000 fewer people will attend.

Discover how to calculate concert attendance based on ticket prices with the linear equation n(p) = 30,000 - 1,000p. Learn how ticket price changes affect attendance using this algebraic formula. Ideal for students in Grades 8-10.

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