Question

For a concert event, there are $30 reserved seat tickets and $20 general admission tickets. There are 1500 reserved seats available, and fire regulations limit the number of paid ticket holders to 2800. The promoter must take in at least $61,000 in ticket sales. Find a system of inequalities describing the different numbers of tickets that can be sold. (Let x be the number of $30 tickets and y be the number of $20 tickets.) number of tickets sold

Answer 1

The system of inequalities is as follows:

30x + 20y ≥ 61,000

x ≤ 1500

x + y ≤ 2800

x ≥ 0

y ≥ 0

Explanation:

The system of inequalities can be explained as follows:

30x + 20y ≥ 61,000 <= Indicating a take in of at least $61,000 in ticket sales.

x ≤ 1500 <= Indicating that 500 reserved seats are available.

x + y ≤ 2800 <= Indicating limit of the paid ticket holders to 2800.

x ≥ 0 <= Indicating ticket x must be equal or greater than 0.

y ≥ 0 <= Indicating ticket y must be equal or greater than 0.