Answer
The water usage varied from 17000 to 26000 gallons.
Work Step by Step
The range of the quarterly bill can be described as $97.74\leq x \leq 150.03$
To find that same range for the water usage, we first must subtract the fixed fee of \$57.07 from both limits:
$97.74-57.07\leq x \leq 150.03-57.07$
$40.67\leq x \leq 92.96$
We have the price rate per 1000 gallons, so we divide that rate by the limits and multiply 1000 to find the total extra gallons consumed.
$40.67\cdot 1000/5.81\leq x \leq 92.96\cdot 1000/5.81$
$7000\leq x \leq16000$
Now, that's the EXTRA gallons that were consumed. There is a fixed number of gallons included in the fixed fee which is 10000, so we add it up to each of the limits to find the true water usage range:
$7000+10000\leq x \leq16000+10000$
$17000\leq x \leq26000$
