Writing Equations for Linear Word Problems

Front

What is the general form of a linear equation used to represent total cost in word problems involving fixed fees and variable costs?

Back

C = mx + b, where C is the total cost, m is the variable cost per unit, x is the number of units, and b is the fixed fee.

Front

In the context of rental services, how do you express the total cost of renting an item that has a fixed fee and a variable cost per hour?

Back

The total cost can be expressed as C = vh + f, where v is the variable cost per hour, h is the number of hours, and f is the fixed fee.

Front

What does the variable 'h' typically represent in linear equations related to rental costs?

Back

In rental cost equations, 'h' usually represents the number of hours the item is rented.

Front

How do you set up an equation to find the total cost of a service that includes a base fee and a per-use charge?

Back

You set up the equation as Total Cost = Base Fee + (Per Use Charge * Number of Uses).

Front

What is the significance of the fixed fee in a linear cost equation?

Back

The fixed fee represents the initial cost incurred regardless of usage, serving as the y-intercept in the equation.

Front

How can you determine the total cost of a service if you know the total charge and the fixed fee?

Back

You can rearrange the equation to find the variable cost by subtracting the fixed fee from the total charge.

Front

What does the variable 'm' represent in the context of a rental car agency's cost equation?

Back

In a rental car agency's cost equation, 'm' typically represents the number of miles driven.

Front

How do you interpret the slope in a linear equation that represents cost?

Back

The slope represents the rate of change in cost per unit of usage, indicating how much the cost increases with each additional unit.

Front

What is the relationship between the total cost and the number of miles driven in a rental scenario?

Back

The total cost increases linearly with the number of miles driven, as represented by the equation: Total Cost = Fixed Fee + (Cost per Mile * Number of Miles).

Front

In the equation 125x + 700 = 1,400, what does 'x' represent?

Back

In this equation, 'x' represents the number of days for which expenses are incurred.