Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 184

A person's accurate typing speed can be approximated by the equation $\displaystyle S = \frac{W - 5e}{10}$, where $S$ is the accurate typing speed in words per minute, $W$ is the number of words typed in ten minutes, and $e$ is the number of errors made.

A job applicant took a 10-minute typing test and was told that she had an accurate speed of 37 words per minute. If she had typed a total of 400 words, how many error did she make?

Solving for the number of errors $e$,


$
\begin{equation}
\begin{aligned}

S =& \frac{W - 5e}{10}
&& \text{Given equation}
\\
\\
10S =& W - 5e
&& \text{Multiply both sides by } 10
\\
\\
5e =& W - 10S
&& \text{Add $5e$ and subtract } 10S
\\
\\
e =& \frac{W - 10S}{5}
&& \text{Divide by } 5
\\
\\
e =& \frac{400 - 10(35)}{5}
&& \text{Substitute } W = 400 \text{ and } S = 35
\\
\\
e =& \frac{400-350}{5}
&& \text{Simplify}
\\
\\
e =& 10
&&

\end{aligned}
\end{equation}
$


She make 10 errors.