Question

body mass index i can be used to determine whether an individual has a healthy weight for his or her height. body mass index is given by the formula, or model, i = \frac{703w}{h^{2}}, where w is weight, in pounds, and h is height, in inches. a persons height is 74 in. determine, in terms of an inequality, the weights w that will keep his body mass index below 30. select the correct choice below and fill in the answer box within your choice. (type an integer or decimal rounded to one decimal place as needed.) a. the weight is {w | w > lb} b. the weight is {w | w = lb} c. the weight is {w | w < lb}

Explanation:

Step1: Substitute values into formula

Given $I=\frac{703W}{H^{2}}$, $H = 74$ and $I<30$. Substitute $H$ into the formula: $I=\frac{703W}{74^{2}}$.

Step2: Set up inequality

Since $I < 30$, we have $\frac{703W}{74^{2}}<30$.

Step3: Solve the inequality for W

First, calculate $74^{2}=5476$. Then the inequality becomes $\frac{703W}{5476}<30$. Multiply both sides by 5476: $703W<30\times5476$. So $703W < 164280$. Divide both sides by 703: $W<\frac{164280}{703}\approx233.7$.

Answer:

C. The weight is $\{W|W < 233.7\text{ lb}\}$