Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5: 75

Answer

For the revenues to exceed the costs, the sales must be higher than 250. The solution set is (x|x $\gt$ 250), or (250, $\infty$) in interval notation.

Work Step by Step

Let x represent the amount of sales. The business receives revenue of 48 per sale. In total, it receives 48 $\times$ x = 48x. The costs are 4000 + 32 per sale. In total, the costs are 4000 + 32 $\times$ x = 4000 + 32x Because revenue needs to exceed the costs, we solve the following inequality. 48x $\gt$ 4000 + 32x 16x $\gt$ 4000 Divide both sides by 16. x $\gt$ 250 For the revenues to exceed the costs, the sales must be higher than 250. The solution set is (x|x $\gt$ 250), or (250, $\infty$) in interval notation.
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