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NAME _____________________ DATE _____________ DUE DATE ___________

ANSWER KEY ATTACHED

6.3 SYSTEMS OF LINEAR INEQUALITIES ~ WORD PROBLEM PRACTICE

1) Jack has to buy pop for family movie night. They need at least 3 litres of Coke. They need at least 6 litres of Dr. Pepper. Jack has enough money to buy a maximum of 12 litres total. What combination of Coke and Dr. Pepper should Jack purchase?

Step 1 - Define your variables. _____ = # of litres of Coke. _____ = # of litres of Dr. Pepper.

Step 2 - Write three inequalities from the paragraph. Use the hints below.

They need at least 3 litres of Coke.

They need at least 6 litres of Dr. Pepper.

Jack has enough money to buy a maximum of 12 litres total.

Step 3 What are the restrictions on the variables? (real numbers, whole numbers, fractions, etc.)

Step 4 - Graph the inequalities.

Step 5 ANSWER THE QUESTION: What combination of Coke and Dr. Pepper should Jack purchase?

2) Buffy the farmer is going to plant corn and beans. Buffy has enough seed to plant 4 acres of corn. She has enough seed to plant 6 acres of beans. Buffy only has 8 acres of land. What combination of corn and beans should Buffy plant?

Step 1 - Define your variables.

Step 2 - Write inequalities.

Buffy has enough seed to plant 4 acres of corn.

She has enough seed to plant 6 acres of beans

Buffy only has 8 acres of land.

Step 3 What are the restrictions on the variables? (real numbers, whole numbers, fractions, etc.)

Step 4 - Draw a graph to determine the region that satisfies all inequalities.

Step 5 ANSWER THE QUESTION: What combination of corn and beans should Buffy plant?

3) Alyssa plays soccer and baseball. She burns 400 calories/hour playing soccer and 50

calories/hour playing baseball. Each week she is willing to spend at most 20 hour exercising

and wishes to burn at least 4000 calories.

a) Define variables x and y for this problem.

Let x represent _________________________________

Let y represent _________________________________

b) Write a system of inequalities and include the restrictions on the variables.

c) Draw a graph to show the time Alyssa could spend on each activity in one week.

Label the axis. Use a scale of 2 on the x-axis and 5 on the y-axis

One possible solution is ( , )

Show that this works in both inequalities. Show your checks in the space below.

4. A company manufactures solar-powered calculators and battery-powered calculators.

In one day, a maximum of 110 solar-powered and 80 battery-powered calculators can be made. Each solar-powered calculator requires 1 work-hour to produce and each battery-powered calculator requires 2 work-hours. There are a maximum of 200 work-hours available each day.

a) Define variables x and y for this problem.

b) Write a system of inequalities and include restrictions on the variables.

c) Draw a graph to determine the region that satisfies all inequalities.

Label the axis. Use a scale of 10 on both axes.

One possible solution is ( , )

Show that this works in both inequalities. Show your checks in the space below.