A-REI Represent and solve equations and inequalities graphically

12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

An arena contains 1200 seats. For an upcoming concert, some seats will be priced $12.00 while other seats are $10.00.

Write and graph a system of linear inequalities to describe the problem.

500 $10 tickets have already been sold, and the total sales must be at least $7200 to make a profit. What are some possible combinations of tickets that can be sold to make a profit?

7. An arena contains 1200 seats. For an upcoming concert, some seats will be priced $12.00 while other seats are $10.00. 500 $10 tickets have already been sold, and the total sales must be at least $7200 to make a profit. What are some possible combinations of tickets that can be sold to make a profit?

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

Since it is not possible toSell negative amount ofTickets, what two other Inequalities should be Considered?

What do these additional inequalitiesTell you about the graph of this system?

Only the quadrant IWill be used.

•If 400 $12 tickets where sold, how many$10 tickets can be sold?

At most 800 $10 tickets.

Not for the problem stated, becauseYou cannot purchase half a ticket.

•Would (700.5, 400) be a solution to this equation?

Can 900 $12 tickets be sold?No, because at least 500tickets must be sold at $10, and that would make the total number of tickets greater than 1200.

What is the intersectionOf the two lines, and what Does it represent in thisSituation?

(700, 500) It representsThe maximum number Of $12 tickets that can be sold.

What is the maximum numberOf $10 tickets that can be sold?What would be the total sales?The Max number of $10 tickets is 1200 (meaning zero$12 tickets were sold). The total sales would be $12,000

What is the y-intercept of thered line? What does it represent in this situation?The y-intercept is 720. If you sold zero $12 tickets then you must sell 720 $10 tickets to make a profit.

What is the intersection of theRed and Blue lines? What does It represent in this situation?

(183⅓, 500) This ordered Pair is represents the minimum amount of tickets that must be sold in order to make a profit. However because you cannot sell ⅓ of a ticket an adjustment must be made.

What is the minimum amount of each ticket that must be sold in order to make a profit? WhatIs the amount of total sales?

184 $12 tickets and 500 $10 tickets.Total Sales: $7208.

What combination of ticket sales Would maximize the profit?What would be the total sales?700 $12 tickets and 500 $10 tickets.Total Sales: $13,400

Does this situation have infinitelyMany ticket combinations?

No, the solutions areWithin a finite area, and all combinations must be whole numbers.