Answer:
- 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.