# 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?

May 29, 2018

The customer drove 1625 miles!

#### Explanation:

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:

$S = 13 d + 0.08 m$

This subtotal is subject to a tax of 4% of the subtotal, which when added to the subtotal gives us the total:

$S + 0.04 S = T$

$1.04 S = T$

color(blue)(1.04(13d+0.08m)=T

The above statement is the general form of the expression we need to find out the number of miles driven. We can now plug in the total, and the number of days utilized:

$1.04 \left(13 \left(4\right) + 0.08 m\right) = 199.68$

Now, we'll divide both sides by the outermost coefficient (1.04) to make the problem a bit simpler:

$\frac{\cancel{1.04} \left(13 \left(4\right) + 0.08 m\right)}{\textcolor{red}{\cancel{1.04}}} = \frac{199.68}{\textcolor{red}{1.04}}$

Now, we simplify:

$13 \left(4\right) + 0.08 m = 192$

$62 + 0.08 m = 192$

$\cancel{62} + 0.08 m \textcolor{R e d}{\cancel{- 62}} = 192 \textcolor{red}{- 62}$

$0.08 m = 130$

Divide both sides by $m$'s coefficient to get the answer:

$\frac{\cancel{0.08} m}{\textcolor{red}{\cancel{0.08}}} = \frac{130}{\textcolor{red}{0.08}}$

$\textcolor{g r e e n}{m = 1625}$