Question

Jayden is deciding between two truck rental companies. Company A charges an initial fee of $85 for the rental plus $1.50 per mile driven. Company B charges an initial fee of $65 for the rental plus $2.50 per mile driven. Let AA represent the amount Company A would charge if Jayden drives xx miles, and let BB represent the amount Company B would charge if Jayden drives xx miles. Write an equation for each situation, in terms of x,x, and determine which company would be cheaper if Jayden needs to drive 5 miles with the rented truck.

Answer 1

• A = 85 +1.50x
• B = 65 +2.50x
• B is cheaper for 5 miles

Explanation:

You want cost equations and the cheaper company for driving 5 miles when A charges $85 plus $1.50 per mile, and B charges $65 plus $2.50 per mile.

(a) Equations

In each case, the cost is the sum of the initial fee and the mileage charge. The mileage charge is the cost per mile, multiplied by the number of miles (x). Using the given fees and costs per mile, we have ...

A = 85 +1.50x

B = 65 +2.50x

(b) Cheaper company

The difference in fees is $85 -65 = $20. The difference in mileage charges is $2.50 -1.50 = $1.00 (per mile). Then the two companies will charge the same for $20/($1 /mile) = 20 miles.

Five miles is less than that "break even" mileage, so the cheaper company will be the one with the lower initial fee. (The graph shows the charges for each company for 5 miles.) For more than 20 miles, the cheaper company is the one with the lower mileage charge.

Company B will be cheaper for a drive of 5 miles.