Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 180

Forensic scientists have determined that the equation $H = 2.9 L + 78.1$ can be used to approximate the height $H$, in centimeters, of an adult on the basis length $L$, in centimeters, of its humerus (the bone extending from the shoulder to the elbow).

According to this formula, what is the length of the humerus of an adult whose height is 168 cm?

Solving for the Humerus $L$,


$
\begin{equation}
\begin{aligned}

H =& 2.9 L + 78.1
&& \text{Given equation}
\\
\\
H - 78.1 =& 2.9 L
&& \text{Subtract } 78.1
\\
\\
\frac{H - 78.1}{2.9} =& L
&& \text{Divide by } 2.9
\\
\\
\frac{168-78.1}{2.9} =& L
&& \text{Substitute } H = 168
\\
\\
\frac{89.9}{2.90} =& L
&& \text{Simplify}
\\
\\
L =& 31 \text{ cm}
&&

\end{aligned}
\end{equation}
$


The length of the Humerus of an adult is $31$ cm.