College Algebra, Chapter 2, 2.5, Section 2.5, Problem 44

Suppose that the value $s$ of a building lot on Los Angeles is jointly proportional to its area $A$ and the quantity of water produced by a well on the property. A 200ft by 300ft lot has a well producing 10 gallons of water per minute, and is valued at \$48,000. What is the value of a 400ft by 400ft lot if the well on the lot produces 4 gallons of water minute?

$s = k AV$ model

$
\begin{equation}
\begin{aligned}
\$ 48000 &= k \left( 200\text{ft} \times 300\text{ft} \right)\left( 10 \text{gallons} \right) && \text{Substitute the given, solve for } k\\
\\
k &= \frac{48000}{(200)(300)(10)} \frac{\$}{\text{ft}^2 \cdot \text{gallons}}\\
\\
k &= \frac{2}{25} \frac{\$}{\text{ft}^2 \cdot \text{gallons}}
\end{aligned}
\end{equation}
$


Then, if $A = 400 \text{ft} \times 400 \text{ft}$ and $V = 4 \text{gallons}$

$
\begin{equation}
\begin{aligned}
s &= \frac{2}{25} \frac{\$}{\text{ft}^2 \cdot \text{gallons}} \left( 400 \text{ft} \times 400 \text{ft} \right) (4 \text{gallons})\\
\\
s &= \$ 51,200
\end{aligned}
\end{equation}
$


The value of the lot is now \$51,200