Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 2 - Section 2.3 - Solving Linear Equations - Exercise Set - Page 142: 83


The equation we set up is: $$\frac{x}{3} + \frac{x}{5} = 16$$ The solution is: $$x = 30$$

Work Step by Step

To set up the equation, we need to understand the terminology of the statement. "One-third of a number" can be translated to "$\frac{1}{3}x$" "One-fifth of a number" can be translated to "$\frac{1}{5}x$" The statement wants these two fractions to be added together, and the result would be $16$. We can then set up the following equation: $$\frac{1x}{3} + \frac{1x}{5} = 16$$ Multiply by the least common denominator to get rid of the fractions. The least common denominator is $15$. $$15(\frac{1x}{3}) + 15(\frac{1x}{5}) = 15(16)$$ Divide out common factors to get: $$5x + 3x = 240$$ Combine like terms: $$8x = 240$$ Solve for $x$: $$x = 30$$
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