How to write a linear equation that will find out how many miles George can travel

Question

George and his grandmother want to visit a different destination each day. He needs to decide which destinations they can visit and still keep the total car rental cost inside of his $245 car rental budget.

The car rental fee for the vehicle George wants is $38.88 per day. Also, there is a mileage fee of $0.43 per mile.

He has researched on the internet about the car and the area. He assumes the rental car gets about 32 miles per gallon, and gas costs $2.88 a gallon.

Answer 1

Let d = the number of days the trip will be scheduled for.

Let m = the total number of miles that will be driven over the duration of the trip.

NOTE that $2.88 per gallon of gas providing 32 miles of travel is equivalent to 2.88/32 = $0.09 per mile driven.

The rental charge of $0.43 per mile can be added to the price per mile of gasoline: 0.43 + 0.09 = $0.52 total price per mile.

Then 38.88d + 0.52m = $245.00. Without knowing the number of days on the trip, we need to stop here. The problem only asked for an equation, and this is what we have derived (in two variables, d and m).

The maximum number of days will be 6. The budget ($245) minus the daily rate will give us the amount that we can use for mileage charges. We can examine this amount for the optimum combination of days and miles, since there are only 6 possibilities.

If a one-day trip is selected, about 388.9 miles can be driven.

If a two-day trip is selected, then an average of about 157.8 miles per day can be driven.

If a three-day trip is selected, then an average of about 80.7 miles per day can be driven.

If a four-day trip is selected,then an average of about 40.2 miles per day can be driven.

If a five-day trip is selected, then an average of about 19.1 miles per day can be driven.

If a six-day trip is selected, then an average of about 3.7 miles per day can be driven.

Either a three-day or a four-day trip seems to be the most practical, providing several days of travel as well as a reasonable amount of mileage.