two kinds of tickets to an outdoor concert were sold: lawn tickets and seat tickets. fewer than 400 tickets in total were sold. solve:a. write an inequality to describe the constraints. specify what each variable represents.b. use graphing technology to graph the inequality. sketch the region on the coordinate plane.c. name one solution to the inequality and explain what it represents in that situation. d. answer the question about the situation: if you know that exactly 100 lawn tickets were sold, what can you say about the number of seat tickets?

Answer:Part a) [tex]x+y < 400[/tex]Part b) The graph in the attached figurePart c) see the explanationPart d) The number of seat tickets sold must be less than 300 ticketsStep-by-step explanation:Part a) write an inequality to describe the constraints. specify what each variable representsLet x ----> number of lawn tickets soldy ----> number of seat tickets soldwe know thatThe sum of the number of lawn tickets sold plus the  number of seat tickets sold must be less than 400 tickets soThe linear inequality that represent this situation is[tex]x+y < 400[/tex]Part b) use graphing technology to graph the inequality. sketch the region on the coordinate planewe have[tex]x+y < 400[/tex]using a graphing toolThe solution is the triangular shaded area of positive integers (whole numbers) of x and ysee the attached figureRemember that the values of x and y cannot be a negative numberPart c) name one solution to the inequality and explain what it represents in that situationwe know thatIf a ordered pair lie on the solution of the inequality, then the ordered pair is a solution of the inequality (the ordered pair must satisfy the inequality)I take the point (200,100)The point (200,100) lie on the triangular shaded area of the solutionVerifySubstitute the value of x and the value of y in the inequality and compare the resultFor x=200,y=100[tex]x+y < 400[/tex][tex]200+100 < 400[/tex][tex]300 < 400[/tex] --> is truesoThe ordered pair satisfy the inequalitythereforeThe ordered pair is a solution of the inequalityThat means ----> The number of lawn tickets sold was 200 and the number of seat tickets sold was 100Part d) if you know that exactly 100 lawn tickets were sold, what can you say about the number of seat tickets?we have thatx=100substitute in the inequality[tex]100+y < 400[/tex]solve for ysubtract 100 both sides[tex]y < 400-100[/tex][tex]y < 300[/tex]thereforeThe number of seat tickets sold must be less than 300 tickets