Solve an Application using a System of Three Linear Equations (Example 4.36)

As a procurement manager reviewing recent vendor invoices, you need to determine the individual unit costs of three different types of office chairs. You decide to model the mixed invoices as a system of linear equations with three variables. Based on the principles of linear systems, which of the following statements correctly describes how you can solve this model?

A small business owner is calculating the individual unit prices of three different types of inventory items by analyzing mixed-order invoices. If the owner models this scenario as a system of linear equations, they must have a minimum of ____ independent invoices (equations) to determine a single, unique price for each of the three items.

A logistics coordinator needs to determine the individual weights of three different shipping container sizes: Small, Medium, and Large. Match each stage of the problem-solving process with the correct description of its function.

In a system of linear equations used to determine the individual unit costs of three different services, the variables in an equation such as ${}5x + 10y + 15z = 450$ represent the known quantities of each service, while the coefficients (5, 10, and 15) represent the unknown unit costs.

A facilities manager is determining the unit costs of three different types of LED lighting fixtures: floodlights, bay lights, and emergency lights. The manager has three invoices, each showing a different combination of these fixtures and their total cost. Arrange the following steps in the correct chronological order to model this scenario as a system of linear equations and solve for the individual unit costs.