1. Day 81 – Applications of Graphing Systems

2. Word Problems
Work with a partner. Let x represent the number of lawn seats and y represent the number of reserve seats.

3. 1. Tickets for the dark Knight concert are $15 for lawn seats and $25 for reserve seats. Each person waiting in line for tickets buy at least one ticket. Some will buy both types of tickets. Write an inequality that represents the amount of money each person will spend.

4. 1. Tickets for the dark Knight concert are $15 for lawn seats and $25 for reserve seats. Each person waiting in line for tickets buy at least one ticket. Some will buy both types of tickets. Write an inequality that represents the amount of money each person will spend.

5. 2. Make a list of five ordered pairs that are solutions of the inequality you wrote.

6. Vary = all positive numbers
2. Make a list of five ordered pairs that are solutions of the inequality you wrote.
Vary = all positive numbers

7. 3. Cross out any ordered pairs you wrote that could not represent a company shouldn't of lawn seat and reserve seat tickets.
Answers may vary

8. 4. Because the concert is expected to be a sellout, each person is limited to buying six tickets. Write an inequality that represents the number of tickets each person will buy.

9. 4. Because the concert is expected to be a sellout, each person is limited to buying six tickets. Write an inequality that represents the number of tickets each person will buy.

10. 5. Cross out any ordered pairs that remain on your list that are not solutions of the inequality you wrote in question 4.

11. 5. Cross out any ordered pairs that remain on your list that are not solutions of the inequality you wrote in question 4. Answers may vary

12. 6. For an ordered pair to remain on your list, what must be true about it?

13. 6. For an ordered pair to remain on your list, what must be true about it? The ordered pair must be true for both inequalities

14. Consumerism
Mrs. Fuentes wants to buy at least 10 books. Each paperback costs an average of $10, and each hardcover book costs an average of $20. Mrs. Fuentes is planning to spend less than $250 on books.
Write a system of linear inequalities that represents this situation. Then graph the solution of the system.
Based on you graph, name three possible combinations of paperback and hardcover books Mrs. Fuentes could buy.

15. Consumerism
a. Let x represent the number of paperback books and y represent the number of hardcover books. The number of books Mrs. Fuentes wants to buy is x + y ≥ 10. The amount she plans to spend is 10x + 20y < 250. So, the system of inequalities that represents the situation is

16. Graph x + y = 10 with a solid line
Graph x + y = 10 with a solid line. Test points on either side of the line, such as (0,0) and (10,10), to see which half-plane to shade. Shade above the line, because the point (10,10) is above the line and makes x + y ≥ 10 true. Then graph 10x + 20y = 250 with a dashed line. Testing points above and below the line shows that the half-plane below the line should be shaded. The solution is the double- shaded region.
10x + 20y = 250
x + y = 10

17. b. Select any three points in the double- shaded region
b. Select any three points in the double- shaded region. The points representing 12 paperback books and 6 hardcover books, 16 paperback books and 0 hardcover books, and 0 paperback books and 10 hardcover books are all within the double- shaded region

18. Word Problem
A chemist will mix a solution that is 2.5% acid with a solution that is 4.8% acid. The total mixture must be at least 45 milliliters and must contain no more than 18 milliliters of acid. How much of each solution will need to be mixed? Write a system of inequalities for this situation. Then use a graphics calculator to graph the boundary lines and to find at least four possible solutions.

19. Answer
Let x represent the amount of 2.5% solution, and let y represent the amount of 4.8% solution. The total mixture must be at least 45 milliliters. Since 2.5% = 0.025, an expression for the amount of acid in the 2.5% solution is 0.025x. Since 4.8% = 0.048, an expression for the amount of acid in the 4.8% solution is 0.048y. The amount of acid in the mixture must not contain more than 18 milliliters.

20. Solve each inequality in the system for y

21. Solve each inequality in the system for y

22. Graph the boundary lines
Graph the boundary lines. Select a point in each of the four regions ( witted by the lines. Test each point in both original inequalities to determine the solution region. The coordinates of the point (170, 150) make both inequalities true, so it is in the solution region. Therefore, one possible solution is to mix 170 milliliters of the 2.5% solution with 150 milliliters of the 4.8% solution.

23. Since x and y represent amounts of a solution, the reasonable domain and range for this situation cannot include negative numbers. The solution region for this problem is contained only in the first quadrant. Any point in the solution region will give the amounts of each solution needed to make the required mixture.

24. The reasonable domain for the problem in Example 2 is all real numbers between 0 and 720, or 0 < x < 720. Explain why this reasonable domain does not include 0 and 720. The reasonable domain for the problem in Example 2 does not make the mixture. alone to include 0 or 720 because neither solution can be used alone to make the mixture