1. COLLEGE ALGEBRA 4.8. System of Inequality Word Problems

2. Do Now: Translate the following into inequalities: X is at most 14 Y is larger than -2 Y is positive Two times a number is less than or equal to zero.

3. Homework Questions? Comments? Confusions? Concerns? ASK ASK ASK!

4. Schedule Today? We have done system of equation word problems////// Let’s do system of inequality word problems!

5. Really Basic: Example One: You need two variables when you are dealing with….. Time Money A certain amount of material and/or items

6. Time: It takes 5 minutes to do A and 6 minutes to do B but you only have 3 hours of free time. Sal wants at least 5 hours of recorded time between 80 minute CDs and 100 minute tapes. **Note: watch the difference in units!*

7. Money: It costs $7.00 to buy A and $12.00 to buy B. You only have $100.00 in cash. You sell lemonade and iced tea at a stand. The lemonade is sold for $3.00 a glass and the ice tea is sold for $4.00 a glass. You want to make at least $400.00 at the stand.

8. Amount of Material/Items You have 24 oz of cocoa butter. Lotion A uses 3 oz and Lotion B uses 4 oz. You use glitter rand ribbons to make a special ornament. Ornament A uses 1 oz of glitter and ½ inch of ribbon and Ornament B uses 2 oz of glitter and ¼ inch of ribbon. You have 20 inches of ribbon and 16 oz of glitter.

9. Further Examples: Ms. Stonebraker has 28 desks + chairs for her boys and girls You sell $12.00 adult tickets and $7.00 student tickets at a theater that seats 500 people. You sell necklaces and bracelets. Your boss wants you to sell at least 500 items.

10. When do you use just one variable? At least 5 cookies and twelve oranges Between 10 and 20 apples At least seven tapes and four CDs, and at most 10 tapes.

11. Let’s Combine it all together! Find the system of inequalities: A carpenter makes bookcases in two different sizes: small and large. It takes 4 hours to make a large bookcase and 2 hours to make a small one. The carpenter can spend only 32 hours per week making bookcases and he must make at least 2 of the large and at least 4 of the small each week.

12. Find the System: A company makes two models of light fixtures, A and B, each of which must be assembled and packed. The time required to assemble model A is 12 minutes and model B takes 18 minutes. It takes 2 minutes to package model A and 1 minute to package model B. Each week there are available 240 hours of assembly time and 20 hours of packaging time.

13. Find the System: A small town is trying to establish a transportation system of large and small vans. It can spend no more than $100,000 for purchasing both sizes of vehicles and no more than $500.00 per month for maintenance. The town can purchase a small van for $10,000 and maintain it for $100.00 per month. Alternatively, the large vans cost $20,000 each and can be maintained for $75.00 per month.

14. You Try! 1) A ski company makes two types of skis and has a fabrication and a finishing department. A pair of downhill skis requires 6 hours to fabricate and 1 hour to finish. A pair of cross-country skis require 4 hours to fabricate and 1 hour to finish. The fabricating department has 108 hours of labor available per day. The finishing department has 24 hours of labor available per day. 2) You are stenciling wooden boxes to sell at a crafts fair. Stenciling takes 2 hours for a small box and 3 hours for a large box. You have no more than 30 hours available but want at least 12 boxes to sell at the fair. 3) A chemical company uses two types of fuel for heating and processing. At least 3,800 gallons of fuel are used each day. The burning of each gallon of #1 fuel leaves a residue of 0.02 pounds of ash and 0.06 pounds of soot. The burning of one gallon of #2 fuel leaves a residue of 0.05 pounds of ash and 0.01 pounds of soot. The factory needs at least 120 pounds of ash and at least 136 pounds of soot each day.

15. Practice Problems Try some on your own/in your table groups As always don’t hesitate to ask me questions if you are confused and/or talk to your tablemates! They are your greatest resource!

16. Exit Ticket: Ms. Stonebraker has $20.00 with her at the supermarket. She needs to buy at least 10 pounds of fruit for a party and a pound of apples cost $1.00 and a pound of pears cost $2.00. Write the inequalities.