A bicycle rental company charges $11$ dollars for the first hour and $6.25$ dollars for each additional hour. Determine the maximum number of hours you can rent a bike if you only have $86$ dollars.
Let $h$ be the number of hours you rent a bike for. Assuming you rent the bike for at least one hour, we can model the price as a function of hours by:
$p(h)=11 + 6.25(h-1)$
Now, if you have 86 dollars, then the maxmimum number of hours for which you can rent a bike can be found by solving the inequailty:
$86 \leq 11 + 6.25(h-1)$
$75 \leq 6.25(h-1)$
$\frac{75}{6.25} \leq h-1$
$12 \leq h-1$
$13 \leq h$
Thus, with $86$ dollars, you can rent a bike for at most $13$ hours.
Method 2:
1 hour cost 11 dollars
2 hours cost $11+6.25 = 17.25$
3 hours cost $11+2(6.25) = 23.5$
Continuing this way...
13 hours cost $11+12(6.25) = 86$
14 hours cost $11+13(6.25) = 92.25$
Thus $13$ hours is the maximum amount of time that we can rent a bike for if we have $86$ dollars.