1. CP Math Word Problems involving inequalities

2. Quiz 6-4 Graph the system of inequalities: 1 2. What is a “solution” to a system of inequalities?

3. This is what “I’m sorry” looks like.

4. Inequality Word Problems Nails cost $5 per pound. Screws cost $10 per pound. You can spend up to $100. can spend up to $100. 1.What type of word problem is this? (total income, total cost, profit, projectile motion, total number) (total income, total cost, profit, projectile motion, total number) 2.Let’s make the x-axis the number of pounds of nails and the y-axis the number of pounds of screws. What is a reasonable domain: What is a reasonable range? x ≥ 0 x ≥ 0 n ≥ 0 s ≥ 0 s ≥ 0

5. Inequality Word Problems Nails cost $5 per pound. Screws cost $10 per pound. You can spend up to $100. can spend up to $100. 3. Write an inequality representing pounds of nails (use x-axis), and pounds of screws (use y-axis) you can buy. and pounds of screws (use y-axis) you can buy. Can you buy negative pounds of nails? 100 ≥ 5x + 10y x ≥ 0 x ≥ 0 Can you buy negative pounds of screws? y ≥ 0 y ≥ 0 100 ≥ 5n + 10s n ≥ 0 s ≥ 0 s ≥ 0

6. Inequality Word Problems Nails cost $5 per pound. Screws cost $10 per pound. You can spend up to $100. can spend up to $100. 4. Graph the inequalities. 100 ≥ 5x + 10y x ≥ 0 x ≥ 0 Any combination of pounds of screws or nails in the shaded region will cost or nails in the shaded region will cost between $0 and $100. between $0 and $100. y ≥ 0 y ≥ 0 10 10 20 20

7. Your turn: 1. Adult tickets cost $7 and student tickets cost $5. The cost of producing the play cost $2500. a)Write an inequality that represents the number of student and adult tickets that need to be sold so that the company doesn’t loose any money. b)What is a reasonable domain? c)What is a reasonable range? 2. Graph the system of inequalities to show all possible combinations of adult and student tickets needed to combinations of adult and student tickets needed to ensure a profit. ensure a profit.

8. Your turn: Apples cost $2 per pound. Peaches cost $3 per pound. You can spend up to $60. can spend up to $60. 3. Write an inequality representing pounds of apples (use x-axis), and pounds of peaches (use y-axis) you can buy. and pounds of peaches (use y-axis) you can buy. 60 ≥ 2a + 3p 4. Write two inequalities to show that you can’t buy 4. Write two inequalities to show that you can’t buy negative numbers of pounds of apples or peaches. negative numbers of pounds of apples or peaches. a ≥ 0 p ≥ 0 5. Graph the system of equations to show all possible combinations of the number of pounds of apples and combinations of the number of pounds of apples and peaches you could buy. peaches you could buy.

9. Word Problems You can work at most 30 hours. Your job as a waiter pays you $15 per hour (after taxes). Your job doing yard work pays you $10 per hour (after taxes). You need to earn You can work at most 30 hours. Your job as a waiter pays you $15 per hour (after taxes). Your job doing yard work pays you $10 per hour (after taxes). You need to earn at least $150 per week to pay for gas, insurance, and your car payment. What kind of problem type is this ? Total income Write the total income equation for this problem: Total income = yard job pay + waiter job pay Total number (of hours) Write the total hours equation for this problem: Total hours = yard job hours + waiter job hours

10. Word Problems You can work at most 30 hours. Waiter pays $15 per hour Yard work pays $10 per hour. You need to earn at least $150 per week. You can work at most 30 hours. Waiter pays $15 per hour Yard work pays $10 per hour. You need to earn at least $150 per week. Total income = yard job pay + waiter job pay Total hours = yard job hours + waiter job hours What are the units of the x-axis? Gardening hours 150 = 10x + 15y 30 = x + y What are the units of the y-axis? Waiter hours

11. Word Problems You can work at most 30 hours. Waiter pays $15 per hour Yard work pays $10 per hour. You need to earn at least $150 per week. You can work at most 30 hours. Waiter pays $15 per hour Yard work pays $10 per hour. You need to earn at least $150 per week. Total income = yard job pay + waiter job pay Total hours = yard job hours + waiter job hours 150 = 10x + 15y 30 = x + y Write a system of inequalities to represent the situation. 30 ≥ x + y 150 ≤ 10x + 15y x ≥ 0 y ≥ 0 x = gardening hours x = gardening hours y = waiter hours y = waiter hours

12. Graph the system of inequalities: x ≥ 0 x ≥ 0 y ≥ 0 y ≥ 0 10 10 15 15 30 ≥ x + y 150 ≤ 10x + 15y x = gardening hours x = gardening hours y = waiter hours y = waiter hours 30 30 what part is shaded? what part is shaded?

13. You can work at most 20 hours per week. Your job as a You can work at most 20 hours per week. Your job as a bagger at Harmon’s pays you $5 per hour (after taxes). Your job as a dog walker pays you $7 per hour (after taxes. You need to earn at least $70 per week to pay for gas, insurance, and your car payment. bagger at Harmon’s pays you $5 per hour (after taxes). Your job as a dog walker pays you $7 per hour (after taxes. You need to earn at least $70 per week to pay for gas, insurance, and your car payment. 6. Write a system of inequalities to represent the situation. Your turn: 7. Graph the system of equations to show the possible combinations of hours you can work at Harmon’s and as a dog walker.

14. Quadratic Inequality Word Problems A ball is dropped from the roof of a 500 foot building. The height (in feet) as a function of time (in seconds) of the ball is given by the following equation: For what period of time is the ball above 400 feet? 400

15. Quadratic Inequality Word Problems A ball is dropped from the roof of a 500 foot building. For what period of time is the ball above 400 feet? 400 Which option do you use to find the time where the two graphs cross?

16. Quadratic Inequality Word Problems A ball is dropped from the roof of a 500 foot building. For what period of time is the ball above 400 feet? 400 2.5 sec From 0 seconds to just less than 2.5 seconds. to just less than 2.5 seconds.

17. Your turn: A ball is dropped from the roof of a 500 foot building. The height of the ball as a function of time is given by: 7. For what period of time will the ball be above 200 feet above ground level? 8. For what period of time will the ball be between 100 and 300 feet?

18. Your turn: An instrumented package that measures air pressure, temperature, and humidity is launched upward using large rubber bands obtained from a medical supply store. The height of the package above ground as a function of time is given by the equation above. 9. For what period of time will the package be above 700 feet? 10. For what period of time will the package be below 300 feet above ground level?

19. The end.

20. Inequality Word Problems y ≤ 0.75x y ≤ 0.75x No more than 75% of the original cost. A clothing store is having a sale. They say that “all hoodies are at least 25% off the regular price”. “all hoodies are at least 25% off the regular price”. 1.Write an inequality representing this sale (use x for regular price and y for sale price (use x for regular price and y for sale price Think about it: Regular price $10, at least 25% off means the price will be what? means the price will be what? What does “sale cost will be no more than 75% of the original price mean? original price mean?

21. Inequality Word Problems y ≤ 0.75x y ≤ 0.75x A clothing store is having a sale. They say that “all hoodies are at least 25% off the regular price”. “all hoodies are at least 25% off the regular price”. “Sale cost will be no more than 75% of the original price.” original price.” Can the sale price be a negative number? What is the smallest price they could charge? 0 ≤ y ≤ 0.75x Can the regular price be a negative number? x ≥ 0 x ≥ 0

22. Inequality Word Problems A clothing store is having a sale. They say that “all hoodies are at least 25% off the regular price”. “all hoodies are at least 25% off the regular price”. 0 ≤ y ≤ 0.75x Compound inequality: y ≥ 0 and y ≤ 0.75x 2. Graph the inequalities on the same graph (use x for regular price and y for sale price (use x for regular price and y for sale price x ≥ 0 x ≥ 0 regular price regular price sale sale price price

23. Inequality Word Problems A clothing store is having a sale. They say that “all hoodies are at least 25% off the regular price”. “all hoodies are at least 25% off the regular price”. 0 ≤ y ≤ 0.75x y ≥ 0 and y ≤ 0.75x 2. Graph the inequalities on the same graph (use x for regular price and y for sale price (use x for regular price and y for sale price x ≥ 0 x ≥ 0 regular price regular price sale sale price price 100 100 75 If x = 100  y = ? If x = 100  y = ?