A car rental company charges $13 dollars a day and 8 cents a mile to rent a car. If a customer rented a car for 4 days and the total bill was $199.68, including a 4% sales tax, how many miles did she drive?

Question

Hazel Anglin · Accepted Answer

The customer drove 1625 miles!

The first thing to do is to write the word problem as a mathematical expression. Let's say the subtotal #S# is equivalent to the number of days driven #d#, multiplied by the cost-per-day, plus the number of miles driven #m#, multiplied by the cost-per-mile: #S=13d+0.08m# When the tax of 4% of the subtotal is added to the subtotal, the total that results is as follows: #S+0.04S=T# #1.04S=T# #color(blue)(1.04(13d+0.08m)=T# The general form of the expression we need to find the miles driven is given by the above statement. We can now plug in the total and the number of days used: #1.04(13(4)+0.08m)=199.68# To simplify the problem, we will now divide both sides by the outermost coefficient (1.04). #(cancel(1.04)(13(4)+0.08m))/color(red)(cancel(1.04))=199.68/color(red)(1.04)# We now simplify: #13(4)+0.08m=192# #62+0.08m=192# #cancel(62)+0.08mcolor(Red)(cancel(-62))=192color(red)(-62)# #0.08m=130# Divide both sides by #m#'s coefficient to get the answer: #(cancel(0.08)m)/color(red)(cancel(0.08))=130/color(red)(0.08)# #color(green)(m=1625)#

Ethan Adkins · Answer

undefined Let $ m $ represent the number of miles driven. The total cost can be represented as:
$$ \text{Total cost} = \text{Base cost (daily rate)} + \text{Mileage cost} $$

Given that the base cost is $13 per day, and the mileage cost is $ 0.08 $ dollars per mile, and the customer rented the car for 4 days, the total cost without tax is:
$$ \text{Total cost} = (13 \times 4) + (0.08 \times m) $$

Adding the 4% sales tax to the total cost, the equation becomes:
$$ 199.68 = (13 \times 4) + (0.08 \times m) + 0.04(13 \times 4) $$

Now, solve for $ m $:
$$ 199.68 = 52 + 0.08m + 0.04 \times 52 $$
$$ 199.68 = 52 + 0.08m + 2.08 $$
$$ 199.68 - 54.08 = 0.08m $$
$$ 145.60 = 0.08m $$
$$ m = \frac{145.60}{0.08} $$
$$ m = 1820 $$

Therefore, the customer drove 1820 miles.