A rents cars at $23.95 plus 20 cents per mile. B rents cars at $22.95 plus 22 cents per mile. For what mileage is A cheaper than B?

Question

what mileage is A cheaper than B

Answer 1

If m is the number of miles then we need to find m such that 23.95+0.20m<22.95+0.22m. Take 22.95 from both sides: 1+0.20m<0.22m. Take 0.20m from each side: 1<0.02m or 0.02m>1. Multiply both sides by 50: m>50. So if mileage is greater than 50 miles, A is cheaper. Let's prove it by putting m=100, then A charges $43.95 and B charges  $44.95. Yes, A is cheaper when the mileage is over 50.