COLLEGE ALGEBRA 4.8. System of Inequalities Word Problems Day Two

Do Now: Determine the system of inequalities: Charlie goes to the mall with $40.00 in his pocket. He wants to buy at least four items of clothing. Pants cost $10.00 and shirts cost $8.00. Ms. Stonebraker wants to make at least 12 batches of cookies for her family reunion. Chocolate Chip uses 3 cups of flour and 2 cups of sugar and Peanut Butter uses 5 cups of flour and 3 cups of sugar. Ms. Stonebraker only has 30 cups of flour and 12 cups of sugar.

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

Today: How do we actually solve a system of inequalities? Well….. We graph it! So let’s graph word problems!

Example One:

Example Two:

You Try!

Example Three: Write a system of inequalities to fit each situation then graph the system. Name three possible solutions in each scenario and what these solutions mean in the context of the problem. Suppose you want to buy some tapes and CDs. You can afford as many as 10 tapes or 7 CDs. You want at least 4 CDs. Each tape holds 24 minutes of music, and each CD holds an hour of music. You want at least 10 hours of total recorded time between the tapes and CDs. Let x be tapes and y be CDs.

Example Three (continued)

Example Four: You are going to make and sell bread. A loaf of Irish soda bread is made with 2 cups of flour and ¼ cup of sugar. Cake bread is made with 4 cups of flour and 1 cup of sugar. You have 16 cups of flour and 3 cups of sugar.

Example Five: You are making and selling skin lotion. A quart of regular skin lotion contains 2 cups of oil and 1 cup of cocoa butter. A quart of extra rich skin lotion contains 1 cup of oil and 2 cups of cocoa butter. You have 24 cups of oil and 18 cups of cocoa butter.

You Try! A doctor offers 15 minutes for routine office visits and 45 minutes for full physicals. The doctor cannot do more than 10 physicals per day and has 9 hours available for appointments each day.

You Try #2: Mrs. Smith grows peaches and apples. At least 500 peaches and 700 apples must be picked daily to meet minimum demands from the buyers. The workers can pick no more than 1200 apples and 1400 peaches daily. The packaging department can handle a maximum of 2,300 fruit per day.

Graph for You Try #2

You Try #3 You are screen-printing T-shirts and sweatshirts to sell at the Polk County Blues Festival and are working with the following constraints. It takes 10 minutes to make a T-shirt It takes 20 minutes to make a sweatshirt You have at most 20 hours to make clothing Supplies for a T-shirt cost $4.00 Supplies for a sweatshirt cost $ You can spend no more than $ on supplies. You want to have at least 50 items to sell at the festival.

You Try #3 Graph

Practice Problems Try some on your own/in small groups As always don’t hesitate to ask me questions if you are confused– and/or ask a tablemate! They are your greatest resource!

Exit Ticket: Write the system of inequalities Ms. Stonebraker wants to enroll in graduate school classes. She wants to enroll in education classes and math classes. Math classes meet for a total of 5 hours each week and education classes meet for a total of 4 hours each week. Ms. Stonebraker can only dedicate 20 hours to her classes and she wants to take at most six total classes. She also wants to make sure to take at least two math classes and one education class.