Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 2 - Equations, Inequalities, and Problem Solving - 2.5 Problem Solving - 2.5 Exercise Set - Page 122: 13

Answer

They have traveled $16.4$ mi from the start.

Work Step by Step

$\bf{\text{l. Familiarize yourself with the problem.}}$ The time given here is not of importance. Given a total distance 20.6 mi, we need to find the distance from the start, x, to satisfy the given condition. $\bf{\text{2. Translate to mathematical language. (This often means writing an equation.)}}$ x is four times larger than (20.5-x), the distance to the finish. $x=4(20.5-x)$ $\bf{\text{3. Carry out some mathematical manipulation. (This often means solving an equation.)}}$ ... simplify the RHS $ x=82.0-4x\qquad$... add 4x to both sides $ 5x=82.0\qquad$... divide both sides with 5 $x=16.4$ mi $\bf{\text{4. Check your possible answer in the original problem.}}$ If they are at $16.4$ mi from the start, they have another $ 20.5-16.4=4.1\quad$ to the finish. Is $16.4$ four times as much as $4.1$? Yes. $\bf{\text{5. State the answer clearly using a complete sentence.}}$ They have traveled $16.4$ mi from the start.
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