Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.5 - Systems of Inequalities - Exercise Set - Page 864: 79


No, the person who is $6$ feet tall and weigh $205$ pounds is not in the healthy weight region.

Work Step by Step

It is known that, $1\text{ feet}=\text{12 inches}$ Let us consider height in feet and convert it into inches as given below: $\begin{align} & \text{6 feet}=\text{6}\times \text{12 inches} \\ & =\text{72 inches} \end{align}$ The coordinates which define the height and weight of a person are $\left( 72,205 \right)$. So, in order to check whether this point lies in the healthy weight region or not, substitute the coordinates for x and y variables respectively in both the provided equations as shown below: Put the values in the first equation as given below: $\begin{align} & 5.3x-y\ge 180 \\ & 5.3\left( 72 \right)-205\ge 180 \\ & 176.6\ge 180 \end{align}$ Which is incorrect. Therefore, the inequality does not hold. Now, put the values in the second equation as given below: $\begin{align} & 4.1\left( x \right)-y\le 140 \\ & 4.1\left( 72 \right)-205\le 140 \\ & 90.2\le 140 \end{align}$ Here, the inequality holds. Therefore, both equations are not satisfied by the coordinates of a person's height and weight, which means that the point does not lie in the healthy weight region. Hence, the person who is $6$ feet tall weighs $205$ pounds is not in the healthy weight region.
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