Chapter A.9, Problem 116AYU

To determine

To find: The Village of Oak Lawn charges homeowners $\$57.07$ per quarter - year plus $\$5.81$ per $1000$ gallons for water usage in excess of $\mathrm{10,000}$ gallons. In $2014$ one homeowner’s quarterly bill ranged from a high of $\$150.03$ to a low of $\$97.74$. The variation of water usage.

Answer to Problem 116AYU

The water usage ranges from $17$ to $26$ per $1000$ gallons.

Explanation of Solution

Given:

The Village of Oak Lawn charges homeowners $\$57.07$ per quarter - year plus $\$5.81$ per $1000$ gallons for water usage in excess of $\$10, 000$ gallons. In $2014$ one homeowner’s quarterly bill ranged from a high of $\$150.03$ to a low of $\$97.74$.

Calculation:

Let $x$ be the amount of water used in $1000$ gallons.

Then $\left(x - 10\right)$ will be the excess of water, since $10$ means $10, 000$ gallons.

$\text{The cost of excess water} = \$5.81\times \left(x-10\right)$

Addition to this, the normal monthly charge is $\$57.07$

Now, we have a function for the amount charged based on the amount of water used.

Let $\text{y}$ be the bill charged.

$\text{i}\text{.e}\text{.}, \text{y} = 57.07 + 5.81 \times \left(x - 10\right)$

$\text{For y} = 150.03$, we get

$150.03 = 57.07 + 5.81\left(x - 10\right)$

$150.03 - 57.07 = 5.81\left(x - 10\right)$

$\frac{92.96}{5.81} = x - 10$

$16 + 10 = x$

∴ $x = 26$

For $\text{y} = 97.74$, we get $97.74 = 57.07 + 5.81\left(x - 10\right)$

$97.74 - 57.07 = 5.81\left(x - 10\right)$

$\frac{40.67}{5.81} = x - 10$

$7 + 10 = x$

∴ $x = 17$

Thus the water usage ranges from $17$ to $20$ per $1000$ gallons.