College Algebra, Exercise P, Exercise P.1, Section Exercise P.1, Problem 12

In Arizonans use an average of 40 gallons of water per person each day.
a.) Find a model for the number of gallons $w$ of water used by $x$ Arizona residents each day.

Since the consumption of water per person each day is 40 gallons, then the number of gallons is represendted by $w = 40x$ model.

b.) Make a table that gives the number of gallons of water used for each 1000-person increase in population, from 0 to 5000. Since the model for the number of gallons of water used by an Arizonan each day is $w = 40x$, so for every...


$
\begin{array}{|c|c|}
\hline\\
x \text{(Person)} & w \text{(Water used)}\\
& \text{in gallons}\\
\hline\\
0 & 40(0) = 0\\
\\
1000 & 40(1000) = 40,000\\
\\
2000 & 40(2000) = 80,000\\
\\
3000 & 40(3000) = 120,000\\
\\
4000 & 40(4000) = 160,000\\
\\
5000 & 40(5000) = 200,000\\
\\
\hline
\end{array}
$


c.) Estimate the population of an Arizona town whose water usage is 140,000 gallons per day.
From the model in part(a), we solve $w = 40x$ for $x$, so...

$
\begin{equation}
\begin{aligned}
\frac{w}{40} &= \frac{\cancel{40}x}{\cancel{40}} && \text{Divide both sides by 40}\\
\\
x &= \frac{w}{40} && \text{model}\\
\\
x &= \frac{140,000}{40} && \text{Substitute } w= 140,000\\
\\
x &= 3500 && \text{Person used 140,000 gallons of water each day}
\end{aligned}
\end{equation}
$