5.4.4 Practice: Modeling: Two-Variable Systems of Inequalities Practice
Algebra I Prescriptive Sem 1
Points Possible:20
Name:

Date:

In this assignment, you may work alone, with a partner, or in a small group. Discuss the results of your work and/or any lingering questions with your teacher.
Your Assignment: Parks and Recreation Workshop Planning
You are helping with the planning of workshops offered by your city's Parks and Recreation department. The director of programs has asked you to purchase snacks for one of the two workshops currently scheduled. Circle the workshop you picked:

Create the Systems of Inequalities
1. Define the variables you will use in your model. (2 points)

2. Write an inequality representing the total cost of your purchase. (3 points)
a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1.

b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.

c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.

3. Write the inequality that models the number of granola bars you need to buy. (1 point)

4. Describe in words what each of your inequalities means. (2 points)
Inequality 1: means...

Inequality 2: means...

Graph the System of Inequalities
5. Graph your system of inequalities. Shade the half plane that represents the solution for each inequality, and then identify the area that represents the solution to the system of inequalities. (5 points: 1 point for each boundary line, 1 point for each correctly shaded half plane, 1 point for identifying the solution)

Interpreting the Graph
6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution. Identify the number of granola bars and pounds of fruit represented by each point, and explain why the point is or is not viable. (4 points: 1 for each point and 1 for each explanation)