A radio station is giving away tickets to a play. They plan to give away tickets to seats that cost $10 or$20. They plan to give away at least 20 tickets, and the total cost of all the tickets can be no more than $300. Make a graph showing how many tickets of each kind can be given away.

The graph shows the solution to the system of inequalities. The shaded region represents all possible combinations of $10 tickets and$20 tickets that the radio station can give away.

1. Let $x$x represent the number of 10 tickets and $$y$$yrepresent the number of20 tickets.

2. The problem states that the radio station will give away at least 20 tickets. This can be represented by the inequality $x + y \ge 20$x+y≥20

3. The problem also states that the total cost of the tickets can be no more than $300. This can be represented by the inequality $10x + 20y \le 300$10x+20y≤300

4. To graph the inequality $x + y \ge 20$x+y≥20, first graph the line $x + y = 20$x+y=20. To do this, find the x-intercept by setting $y = 0$y=0 and solving for $x$x: $x + 0 = 20$x+0=20, so $x = 20$x=20. Find the y-intercept by setting $x = 0$x=0 and solving for $y$y: $0 + y = 20$0+y=20, so $y = 20$y=20. Plot the points $(20, 0)$(20,0) and $(0, 20)$(0,20) and draw a line through them. Since the inequality is $\ge$≥, shade the region above the line.

5. To graph the inequality $10x + 20y \le 300$10x+20y≤300, first graph the line $10x + 20y = 300$10x+20y=300. To do this, find the x-intercept by setting $y = 0$y=0 and solving for $x$x: $10x + 20(0) = 300$10x+20(0)=300, so $x = 30$x=30. Find the y-intercept by setting $x = 0$x=0 and solving for $y$y: $10(0) + 20y = 300$10(0)+20y=300, so $y = 15$y=15. Plot the points $(30, 0)$(30,0) and $(0, 15)$(0,15) and draw a line through them. Since the inequality is $\le$≤, shade the region below the line.

6. The solution to the system of inequalities is the region where the shaded areas of both inequalities overlap. This region represents all possible combinations of $10 tickets and$20 tickets that the radio station can give away.