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# A car rental company charges $40 a day with no additional mileage fees. Another company charges$24 each day plus \$0.16 per mile. How many miles would have to be driven in one day for the first company to offer the better deal?

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Let $x$ be the number of miles driven in a one day. Then an equality that models the conditions of the problem is $40\leq24+0.16x$.

Using properties of inequality, the number of miles that should be driven for the first company to offer the better deal is:

\begin{aligned} \because 24+0.16x&>40\\ \Rightarrow 24-24+0.16x&>40-24\\ \Rightarrow\hspace{1.55cm} 0.16x&>16\\ \Rightarrow\hspace{0.5cm} (0.16x)(100)&>(16)(100)\\ \Rightarrow\hspace{1.8cm} 16x&>1600\\ \Rightarrow\hspace{2.2cm} x&>100\textrm{ miles} \end{aligned}

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