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.