# A car company charges a flat rate for hiring a car and also charges at per mile rate for usage. Its charge for 18 miles is $18.79 and for 25 miles is $22.29. What is the charge per mile and flat rate?

Oct 25, 2016

Charges per mile are $0.50 and flat rate is $9.79.

#### Explanation:

Let $x$=charge per mile
$y$= flat rate

$18 x + y = 18.79$
$25 x + y = 22.29$

From first equation, we get $y = 18.79 - 18 x$. Using substitution...

$25 x + \left(- 18 x + 18.79\right) = 22.29$

or $7 x = 22.29 - 18.79 = 3.50$

i.e. $x = \frac{3.50}{7} = 0.50$

Substitute $0.50$ for $x$ in any equation

$18 \left(0.50\right) + y = 18.79$

or $9.00 + y = 18.79$

i.e. $y = 18.79 - 9.00 = 9.79$