Comparing two linear functions

Question

Brandon is deciding between two truck rental companies. Company A charges an initial fee of $75 for the rental plus $2 per mile driven. Company B charges an initial fee of $35 for the rental plus $3 per mile driven. Let A represent the amount Company A would charge if Brandon drives x miles, and let B represent the amount Company B would charge if Brandon drives x miles. Write an equation for each situation, in terms of x, and determine which company would be cheaper if Brandon needs to drive 45 miles with the rented truck.

Answer 1

First we need to determine a variable and what it represents. So we'll let x equal miles driven. And y will be the cost.

For Company A, the fixed cost is $75 and it costs $2 per mile. Whenever you see something with units like dollars per mile or miles per hour, that number is the slope in your linear equation. So the equation for the cost of using Company A will be y = 2x + 75.

Likewise the cost for using Company B will be y = 3x + 35.

To determine which Company will be the cheapest to use if we drive 45 miles, we plug 45 in for x in both equations and see which equation has the smallest value for y.

Company A

y = 2(45) + 75

y = $165

Company B

y = 3(45) + 35

y = $170

So Company A will cost the least if we drive 45 miles.