Question

A rental car cost $25 plus a fixed charge per mile driven. The total charge for 210 miles of use was $67. Write an equation for the cost, C (in dollars), in terms of the miles driven, x.

Answer 1

To start, we know the basic equation from what us given:

$c = 25 + mx$
And we want to find m. Fortunately, we have some numbers to plug in to find m. We can make an equation like this
$67 = (210)m + 25$
by taking the amount charged and the amount of miles driven to get that charge given in the original problem.

Now we solve.
$67 - 25 = 210m + 25 - 25 \\ 42 = 210m \\ \frac{42}{210} = \frac{210}{210} m \\ \frac{1}{5} = m$
Now we can put that in our equation to finish it.
$c = \frac{1}{5} x + 25$
And that is the final equation