QuestionFind the weight range $w$ for a healthy BMI (19-25) at heights: (a) 75 in., (b) 74 in., (c) 78 in. Round to nearest lb.

Studdy Solution

STEP 1

Assumptions1. The formula for BMI is given as $\mathrm{BMI}=\frac{704 \times \text { (weight in pounds) }}{\text { (height in inches) }^{}}$ . A healthful BMI is between19 and253. We need to find the weight range $w$ that gives a healthful BMI for each height4. The heights are given as75 in.,74 in., and78 in.

STEP 2

First, we need to find the weight range for a healthful BMI. We can do this by rearranging the BMI formula to solve for weight.
$Weight = \frac{BMI \times (height\, in\, inches)^2}{704}$

STEP 3

Now, we need to find the weight range for a BMI of19 and25 for each height. Let's start with a height of75 inches.
For a BMI of19 $Weight = \frac{19 \times (75)^2}{704}$ For a BMI of25 $Weight = \frac{25 \times (75)^2}{704}$

STEP 4

Calculate the weight range for a height of75 inches.
For a BMI of19 $Weight = \frac{19 \times (75)^2}{704} \approx141\, lbs$ For a BMI of25 $Weight = \frac{25 \times (75)^2}{704} \approx187\, lbs$

STEP 5

Repeat the same process for a height of74 inches.
For a BMI of19 $Weight = \frac{19 \times (74)^2}{704}$ For a BMI of25 $Weight = \frac{25 \times (74)^2}{704}$

STEP 6

Calculate the weight range for a height of74 inches.
For a BMI of19 $Weight = \frac{19 \times (74)^2}{704} \approx138\, lbs$ For a BMI of25 $Weight = \frac{25 \times (74)^2}{704} \approx184\, lbs$

STEP 7

Repeat the same process for a height of78 inches.
For a BMI of19 $Weight = \frac{19 \times (78)^2}{704}$ For a BMI of25 $Weight = \frac{25 \times (78)^2}{704}$

STEP 8

Calculate the weight range for a height of78 inches.
For a BMI of19 $Weight = \frac{19 \times (78)^2}{704} \approx146\, lbs$ For a BMI of25 $Weight = \frac{25 \times (78)^2}{704} \approx194\, lbs$ So, for a height of75 inches, the weight range is approximately141 to187 lbs. For a height of74 inches, the weight range is approximately138 to184 lbs. And for a height of78 inches, the weight range is approximately146 to194 lbs.

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