Final answer:
The question deals with creating linear equations to represent total costs, combining both fixed fees and per-hour charges. Dependent variables are the total costs, and independent variables are the number of hours of service use. Formulas like C = $32x + $31.50 for word processing or F = $12.50x + $25 for equipment rental illustrate this relationship.
Step-by-step explanation:
The question provided pertains to creating an equation to represent the total cost based on a service that has both a fixed fee and a per-hour charge. We can approach this by first identifying the dependent and independent variables. In this context, the dependent variable is the total cost, and the independent variable is the number of hours the service or equipment is rented or used.
To find the appropriate equation, we start by taking the fixed fee and adding the product of the hourly rate and the number of hours. For Aaron's Word Processing Service, the total cost (C) is represented by the equation C = $32x + $31.50, where x represents the number of hours of work. Similarly, for the vacation resort's scuba equipment rental, the total fee (F) can be expressed by the equation F = $12.50x + $25, with x representing the number of hours the equipment is rented.
By writing such equations, we obtain linear equations that help predict the total cost or fee based on the time used. These calculations are essential for budgeting and pricing strategies for both consumers and businesses.