Question

Car Rental Cost A car rental company offers two plans for renting a car.

Plan A:$\mathrm{\backslash (}30\mathrm{per}\mathrm{day}\mathrm{and}10\cancel{c}\mathrm{per}\mathrm{mile}$

Plan B:$\mathrm{\backslash )}50\text{perdaywithfreeunlimitedmileage}$

For what range of miles will plan B save you money?

Short answer

The number of miles driven should be less than 200.

Step-by-step solution

Step 1. Apply the concept of Solving linear inequalities.

An inequality looks like an equation, except that in the place of the equal sign is one of the symbols, $<,>,\le ,\ge$.

Example of an inequality is $4x+7\le 19$.

An inequality is linear if each term is constant or a multiple of the variable. To solve a linear inequality, isolate the variable on one side of the inequality sign.

Step 2. Find the inequality.

Let x be the number of miles driven.

Hence, the following are obtained:

$\begin{array}{l}\text{CostwithplanA:30+0.10x}\\ \text{CostwithplanB:50}\end{array}$

To save the money, B should be less than A. Hence,

$50<30+0.10x$

Step 3. Simplify the inequality.

Simplify the inequality $50<30+0.10x$. Therefore,

$\begin{array}{l}50<30+0.10x\\ \Rightarrow 50-30<0.10x\text{(subtract30)}\\ \Rightarrow 20<0.10x\\ \Rightarrow \frac{20}{0.10}<x\text{(divideby0.10)}\\ \Rightarrow 200<x\end{array}$

Hence, the number of miles driven should be less than 200.