Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 176

The pressure at a certain depth in the ocean can be approximated by the equation $\displaystyle P = \frac{1}{2} D + 15$, where $P$ is the pressure in pounds per square inch and $D$ is the depth in feet.

Find the depth of a diver when the pressure on the diver is $45$ lb/in$^2$.

We solve for $D$ (depth),


$
\begin{equation}
\begin{aligned}

P =& \frac{1}{2} D + 15
&& \text{Given equation}
\\
\\
P - 15 =& \frac{1}{2} D
&& \text{Subtract } 15
\\
\\
2(P - 15) =& D
&& \text{Multiply both sides by } 2
\\
\\
2P - 30 =& D
&& \text{Apply Distributive Property}
\\
\\
2(45) - 30 =& D
&& \text{Substitute } P = 45
\\
\\
90-30 =& D
&& \text{Simplify}
\\
\\
D =& 60 \text{ ft}
&&

\end{aligned}
\end{equation}
$


The depth of the diver is $60$ ft.

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