Systems of Equations and Inequalities Applications Word Problems

1. Solve the system of equations by elimination.

7x + 8y = -55
4x + 5y = -34

2. Ron and Kathy are telemarketers. Ron contacts potential home buyers and is paid $30.00 for each buyer he gets to work with a realtor at the company. Kathy contacts potential sellers and is paid $65.00 for each seller she gets to discuss listing a home with the company. If their total income for 17 successful contacts was $860.00 how many did Ron set up?

Set up a system of equations to describe this situation. Solve the system of equations to find the solution

3. Graph the following system of inequalities using MathGV.

4x + 3y > 1
-3x + 2y < 2

For the purposes of using MathGV, let blue symbolize a solid line and green a broken line.

Problems 4 and 5 are based on the following information.

A psychology department buys mice and rats for experiments. They have cages for at most 300 mice and rats. Each mouse costs $1 to purchase and each rat costs $2 to purchase. The department has a total of $400 available to purchase the animals. Each mouse can be used for 73 experiments and each rat can be used for 111 experiments. How many mice and rats should be bought in order to maximize the number of experiments that can be performed?

4. Identify and graph each of the following.

a. The inequality which expresses the limitation for the number of cages they have to house animals.
b. The inequality which expresses the limitation for the amount of money they have to spend purchasing the mice and rats.
c. Identify the objective function that will be used to maximize the number of experiments they can perform.

5. Determine the combination of mice and rats that allows the department to do the maximum number of experiments.

a. List all of the vertices of the region bounded by the inequalities in #4. Because this is such a large graph for MathGV, it isn't necessary for you to submit a picture for this one. However, to receive full credit, you must list all vertices.

b. Use the objective function to test the vertices from part a and determine the combination of mice and rats that allows the department to do the maximum number of experiments. Show your work and clearly label your final answer in terms of the original problem.