## Precalculus (6th Edition) Blitzer

No, the person who is $5$ feet $8$ inches tall and weighs $135$ pounds is not in the healthy weight region.
It is known that, $1\text{ feet}=\text{12 inches}$ Let us consider height in feet and convert it into inches as shown below: \begin{align} & \text{5 feet 8 inches}=\text{5}\times \text{12 inches}+\text{8inches} \\ & =\text{68 inches} \end{align} The coordinates which define the height and weight of a person are $\left( 68,135 \right)$. So, in order to check whether this point lies in the healthy weight region or not, substitute the coordinates for the 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( 68 \right)-135\ge 180 \\ & 225.4\ge 180 \end{align} And the inequality holds. Now, put the values in the second equation as given below: \begin{align} & 4.1\left( x \right)-y\le 140 \\ & 4.1\left( 68 \right)-135\le 140 \\ & 143.8\le 140 \end{align} Which is incorrect. Thus, the inequality does not hold. Therefore, both equations are not satisfied by the coordinates of a person's height and weight, which means that the provided point does not lie in the healthy weight region. Hence, a person who is $5$ feet $8$ inches tall and weighs $135$ pounds is not in the healthy weight region.