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NAME _____________________ DATE _____________ DUE DATE ___________6.3 SYSTEMS OF LINEAR INEQUALITIES ~ WORD PROBLEM PRACTICE1) 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.
ANSWER KEY ATTACHED
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.