Tickets to a concert cost $6 for reserved seats and $4 for general admission. If receipts must be at least $10,200 to meet expenses, graph an inequality that shows the possible ways that the box office can sell reserved seats ( x ) and general admission tickets ( y ). Graph the inequality for nonnegative values of x and y .

Question

Quizplus · Accepted Answer

Let x be the number of reserved seats sold and y be the number of general admission tickets sold.

The total receipts will be the sum of the amounts earned from reserved seats and general admission tickets, which can be expressed as:

6x + 4y ≥ 10,200

Simplifying this inequality, we get:

3x + 2y ≥ 5,100

To graph this inequality, we can first graph the line 3x + 2y = 5,100, which represents the boundary of the inequality:
- Plot the x-intercept: (1, 0)
- Plot the y-intercept: (0, 2,550)
- Connect the two points

Since we want to graph the inequality for nonnegative values of x and y, we shade the region above the line (y ≥ (-3/2)x + 2,550) and to the right of the y-axis (x ≥ 0).
The resulting graph matches choice C.

Tickets to a Concert Cost $6 for Reserved Seats and $4