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Example

Which is the better value when renting a vehicle?

Rent-A-Car charges $29.95 per day and 43 cents per mile.
Auto-Loaner charges $45 per day and 32 cents per mile.


Understand

Find the value at which the costs are the same and then evaluate which plan is most advantageous.

Let m = the total miles to be driven.
Let c = the total rental cost for each company.

Rent-A-Car:     c = 29.95 + 0.43m
Auto-Loaner:    c = 45 + 0.32m


Substitution Method

Since both equations name costs in terms of c, set them equal to each other and solve for miles.  Solving for m will show us when the costs will be the same.

29.95 + 0.43m = 45 + 0.32m


Solution

For distances under 137 miles, Rent-A-Car is the better value.
For distances over 137 miles, Auto-Loaner is the better value.