A popular band is trying to raise at least $20,000 for charity by holding multiple concerts at a park. It plans to sell tickets at $25 each. For each 2-hour concert, the band would need to pay the park $1,250 in fees for security, cleaning, and traffic services.

Question

A popular band is trying to raise at least $20,000 for charity by holding multiple concerts at a park. It plans to sell tickets at $25 each. For each 2-hour concert, the band would need to pay the park $1,250 in fees for security, cleaning, and traffic services.

The band needs to find the combinations of number of tickets sold, t, and number of concerts held, c, that would allow it to reach its fundraising goal.
Write an inequality to represent the constraints in this situation.

Answer 1

The inequality that represents the constraints in this situation is:

25t - 1250c ≥ 20000

Where:
t represents the number of tickets sold
c represents the number of concerts held
25t represents the total revenue from ticket sales (since each ticket is sold at $25)
1250c represents the total expenses paid to the park for each concert
20000 represents the fundraising goal that the band wants to reach.

Answer 2

Let's write the inequality step by step.

Let t represent the number of tickets sold and c represent the number of concerts held.

The fundraising goal is at least $20,000, so we can set up the inequality:

25t * c >= 20,000

Now, let's add the constraint for the park fees. For each 2-hour concert, the band would need to pay the park $1,250 in fees. So for c concerts, the total fees would be 1,250 * c. We can include this constraint in the inequality:

25t * c - 1,250c >= 20,000

This inequality represents the constraints in this situation.

Answer 3

To represent the constraints in this situation, we need to take into account the ticket prices, the number of tickets sold, the number of concerts held, and the fees paid to the park.

Let's break it down:

1. The total amount raised from ticket sales for each concert is given by: 25t.
2. The total amount raised from ticket sales for all concerts is given by: 25t * c.
3. The total amount paid to the park for each concert is given by: 1250.
4. The total amount paid to the park for all concerts is given by: 1250 * c.

The inequality to represent the constraints is:
25t * c - 1250 * c ≥ 20000

Explanation: The left side of the inequality represents the total amount raised from ticket sales minus the total amount paid to the park for all concerts. The right side represents the fundraising goal, which is the minimum of $20,000. This inequality ensures that the band raises at least $20,000 after subtracting the park fees.