College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 1 - Equations and Inequalities - Exercise Set 1.7 - Page 198: 122

Answer

One must drive $more$ $than$ $100$ miles for Basic to be a better deal.

Work Step by Step

First, we model the cost of each rental with the following equations: $$Basic_{cost} = 50 + 0.2m$$ $$Continental_{cost} = 20 + 0.5m$$ where $m$ represents the amount of miles to be driven. The exercise asks for the amount of miles needed for Basic to be a better deal than Continental. In other words, at what $m$ Continental becomes greater than Basic: $$Continental_{cost}\gt Basic_{cost}$$ $$20 + 0.5m \gt 50 + 0.2m$$ By solving for $m$: $$0.5m - 0.2m \gt50 - 20$$ $$0.3m \gt 30$$ $$m\gt 100$$
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