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 revenue can be expressed as:
Revenue = 6x + 4y
The expenses must be at least $10,200, so we have:
6x + 4y >= 10200
Dividing both sides by 2, we get:
3x + 2y >= 5100
Simplifying, we get:
y >= -3/2x + 2550
This is the graph of a line with a slope of -3/2 and a y-intercept of 2550. We can plot this line using two points: (0, 2550) and (1700, 0), since at x=0, y=2550 and at y=0, x=1700. 
However, we are only interested in nonnegative values of x and y, so we need to shade the region above or on the line. This represents all the possible ways the box office can sell reserved seats and general admission tickets to earn at least $10,200 in revenue. Choice C correctly shows this region.

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