### Example A.8.

The equation \(w = 6h\) gives Loren’s wages, \(w\text{,}\) in terms of the number of hours she works, \(h\text{.}\) How many hours does Loren need to work next week if she wants to earn $\(225\text{?}\)

## Solution.

We know that \(w = 225\text{,}\) and we would like to know the value of \(h\text{.}\) We substitute the value for \(w\) into our equation and then solve for \(h\text{.}\)

\begin{align*}
w \amp= 6h\amp\amp \blert{\text{Substitute 225 for }w.}\\
\alert{225} \amp= 6h\amp\amp \blert{\text{Divide both sides by } 6.}\\
\frac{225}{\alert{6}}\amp = \frac{6h}{\alert{6}}\amp\amp \blert{\text{Simplify.}}\\
375.5\amp = h
\end{align*}

Loren must work \(37.5\) hours in order to earn $\(225\text{.}\) In reality, Loren will probably have to work for \(38\) hours, because most employers do not pay for portions of an hour’s work. Thus, Loren needs to work for \(38\) hours.