Jon rented a car from a company that charged...

Question

Jon rented a car from a company that charged a daily rental fee and a mileage charge. He rented the car for 6 days and drove 400 miles and was charged $410. His friend Amanda later rented the same car for 5 days and drove 280 miles and was charged $323. What was the daily rental charge? How much did the company charge per mile?

Answer 1

So a company charges a fee per day and a fee per mile of rental. Jon rented for 6 days and 400 miles, and was charged $410, so we can come up with:

 

6d + 400m = 410

 

where d is the amount of money charged per day and m is the amount of money charged per mile.

 

Amanda rented for 5 days and 280 miles and was charged $323, so we can come up with:

 

5d + 280m = 323

 

So now we have 2 equations that each have 2 different variables, so we need to eliminate one of the variables. So what we can do is this: we multiply all of the terms in the first equation by 5 and all of the terms in the second equation by 6, so that both equations contain 30d, like this:

 

5 x [6d + 400m = 410] = 30d + 2000m = 2050

 

and

 

6 x [5d + 280m = 323] = 30d + 1680m = 1938

 

So now we have 2 new equations that both contain 30d, so we can subtract one from the other to eliminate 30d, like this:

 

            30d + 2000m = 2050

      -  ( 30d + 1680m = 1938)

    _________________________

             0   +   320m = 112

 

So now we are left with:

 

320m = 112

 

and solving for m, we get:

 

m = 0.35

 

So the mileage charge is $0.35. To find the daily rental charge, you can plug in what we found for m into one of the original equations and solve for d:

 

5d + 280m = 323

5d + 280(0.35) = 323

5d + 98 = 323

5d = 225

d = 45

 

And so the daily rental charge is $45.