Example2.2.14

Ann has budgeted a maximum of \(\$300\) for an appliance repair. The total cost of the repair can be modeled by \(89+110(h-0.25)\text{,}\) where \(\$89\) is the initial cost and \(\$110\) is the hourly labor charge after the first quarter hour. Is \(2\) a solution for \(h\) in the inequality \(89+110(h-0.25)\le 300\text{?}\)

To determine if \(h=2\) satisfies the inequality \(89+110(h-0.25)\le 300\text{,}\) we will replace \(h\) with \(2\) and check if the statement is true or false:

\begin{align*} 89+110(h-0.25)\amp\le 300\\ 89+110(\substitute{2}-0.25)\amp\stackrel{?}{\le} 300\\ 89+110(1.75)\amp\stackrel{?}{\le} 300\\ 89+192.5\amp\stackrel{?}{\le} 300\\ 281.5\amp\stackrel{\checkmark}{\le} 300 \end{align*}

Thus \(2\) is a solution for \(h\) in the inequality \(89+110(h-0.25)\le 300\text{.}\) In context, this means that Ann would stay within her \(\$300\) budget if \(2\) hours of labor were performed.

in-context