# Sunset rents an SUV at $21.95 plus$0.23 per mile. Sunrise rents the same vehicle for $24.95 plus$0.19 per mile. For what mileage is the cost the same?

Oct 23, 2015

I found $75$ miles

#### Explanation:

The linear model describing the two situations are:
Sunset: $y = 0.23 x + 21.95$
Sunrise: $y = 0.19 x + 24.95$
where $x$ is miles and $y$ the cost:
setting them equal you get:
$0.23 x + 21.95 = 0.19 x + 24.95$
giving:
$0.23 x - 0.19 x = 24.95 - 21.95$

$0.04 x = 3$
$x = \frac{3}{0.04} = 75$ miles