Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 3 - Section 3.6 - Graphing Linear Inequalities in Two Variables - Exercise Set - Page 266: 47

Answer

a) $30x + .15y \leq 500$ b) Please see the graph, made using graphing software c) We cannot have a negative number of days, and we cannot have a negative number of miles. That is why the grid shows only quadrant I.

Work Step by Step

a) 500 max budget 30 dollars per day (x) .15 dollars per mile (y) $500 \geq 30x+.15y$ $30x + .15y \leq 500$ b) $30x + .15y \leq 500$ Let $x=0$ $30x + .15y \leq 500$ $30*0 + .15y \leq 500$ $.15y \leq 500$ $.15y/.15 \leq 500/.15$ $y \leq 3333.33$ Let $y=0$ $30x + .15y \leq 500$ $30x + .15*0 \leq 500$ $30x \leq 500$ $30x/30 \leq 500/30$ $x \leq 16.66$ $(0, 3333.33)$ and $(16.66,0)$ are on the line. Use $(0,0)$ to determine what side of the line to shade. $30x + .15y \leq 500$ $30*0 + .15*0 \leq 500$ $0 + 0 \leq 500$ $0 \leq 500$ is true, so we shade the side of the line with the point $(0,0)$.
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