Budget charges 29.95 for the day and 0.55 per mile driven...

Budget charges $\$ 29.95$ for the day and $\$ 0.55$ per mile driven to rent a 10 -foot moving truck. a. Let $B$ be the cost of renting a 10 -foot moving truck from Budget for a day and driving the truck $m$ miles. Write an equation for the cost of renting from Budget. b. How much would it cost to rent a 10 -foot truck from Budget if you were to drive it 75 miles? c. How many miles could you drive the truck if you could pay only $\$ 100$ for the rental?

Budget charges $\$ 29.95$ for the day and $\$ 0.55$ per mile driven to rent a 10 -foot moving truck.
a. Let $B$ be the cost of renting a 10 -foot moving truck from Budget for a day and driving the truck $m$ miles. Write an equation for the cost of renting from Budget.
b. How much would it cost to rent a 10 -foot truck from Budget if you were to drive it 75 miles?
c. How many miles could you drive the truck if you could pay only $\$ 100$ for the rental?

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Key Concepts

Linear Equations

Linear equations describe relationships where one variable depends on another in a constant rate, often expressed as y = mx + b. In the context of cost problems, this formulation allows us to combine fixed fees (the y-intercept) with variable costs (the slope) that change proportionally with usage or mileage.

Fixed and Variable Costs

Fixed costs are constant fees that do not change with the level of usage, while variable costs depend on the number of units used. When modeling rental charges or similar scenarios, the fixed cost represents an initial fee, and the variable cost represents an additional charge per unit, such as per mile in this context.

Function Evaluation

Function evaluation involves substituting a specific value of the independent variable into the linear equation to calculate the corresponding result. This process is essential for determining the total cost when a particular number of miles or units is given.

Solving for a Variable

Solving for a variable in a linear equation involves isolating the variable of interest on one side of the equation. This technique is particularly useful when you know the total cost and need to determine an unknown quantity such as the number of miles driven, by reversing the relationship expressed in the linear model.

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