# Rachel drove 200 miles using 9 gallons of gas. At this rate, how many gallons of gas would she need to drive 420 miles?

Dec 9, 2016

Rachel would need 18.9 gallons to drive 420 miles at the same rate of consumption.

#### Explanation:

We can state the problem as a ratio:

$9$ gallons $: 200$ miles is the same as $x$ gallons $: 420$ miles

Write this as an equation gives:

$\frac{9 g a l l o n s}{200 m i l e s} = \frac{x}{420 m i l e s}$

We can now solve for $x$:

$\left(420 m i l e s\right) \cdot \frac{9 g a l l o n s}{200 m i l e s} = \left(420 m i l e s\right) \cdot \frac{x}{420 m i l e s}$

$\left(420 \cancel{m i l e s}\right) \cdot \frac{9 g a l l o n s}{200 \cancel{m i l e s}} = \left(\cancel{420} \cancel{m i l e s}\right) \cdot \frac{x}{\cancel{420} \cancel{m i l e s}}$

$420 \cdot \frac{9 g a l l o n s}{200} = x$

$x = \frac{3780 g a l l o n s}{200}$

$x = 18.9 g a l l o n s$