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 complete question is;

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.

(25t)c - 1250 ≥ $20,000

Step-by-step explanation:

We are told the band is trying to raise at least $20,000.

It's trying to sell tickets at $25 each.

We are told that they pay the park $1,250 in fees for security, cleaning, and traffic services.

Now, expenses for each concert is $1,250.

Now, we are told that the number of tickets sold is t, and number of concerts held, c.

Thus, total amount that can be realized for "c" number of concerts is;

A = (25t)c

Now, expenses for each concert is $1,250.

Thus, total profit for "c" number of concerts is;

P = (25t)c - 1250

Now, they are trying to raise at least $20,000. Meaning greater than or equal to $20,000.

Thus, the profit must be greater than or equal to $20,000.

Thus, the inequality is;

(25t)c - 1250 ≥ $20,000