QuestionFind the weight range $w$ (to the nearest pound) for a healthful BMI (19-25) at heights: (a) 72 in, (b) 75 in, (c) 78 in using $\mathrm{BMI}=\frac{704 \times(\text { weight })}{(\text { height })^{2}}$ .

Studdy Solution

STEP 1

Assumptions1. The formula for BMI is given by $\mathrm{BMI}=\frac{704 \times(\text { weight in pounds })}{{\text { (height in inches })^{}}^{}}$ . A healthful BMI is between19 and25.
3. We are asked to find the weight range for heights72 in.,75 in., and78 in.

STEP 2

First, we need to rearrange the BMI formula to solve for weight. $\text { weight in pounds } = \frac{\mathrm{BMI} \times (\text { height in inches })^{2}}{704}$

STEP 3

Now, we will use the rearranged formula to find the weight range for a height of72 in. We will do this twice, once for a BMI of19 and once for a BMI of25.
$\text { weight in pounds } = \frac{19 \times (72)^{2}}{704}$ $\text { weight in pounds } = \frac{25 \times (72)^{2}}{704}$

STEP 4

Calculate the weight range for a height of72 in.
$\text { weight in pounds } = \frac{19 \times (72)^{2}}{704} =136 \, \text{pounds}$ $\text { weight in pounds } = \frac{25 \times (72)^{2}}{704} =180 \, \text{pounds}$

STEP 5

Repeat the process for a height of75 in.
$\text { weight in pounds } = \frac{19 \times (75)^{2}}{704}$ $\text { weight in pounds } = \frac{25 \times (75)^{2}}{704}$

STEP 6

Calculate the weight range for a height of75 in.
$\text { weight in pounds } = \frac{19 \times (75)^{2}}{704} =142 \, \text{pounds}$ $\text { weight in pounds } = \frac{25 \times (75)^{2}}{704} =188 \, \text{pounds}$

STEP 7

Repeat the process for a height of78 in.
$\text { weight in pounds } = \frac{19 \times (78)^{2}}{704}$ $\text { weight in pounds } = \frac{25 \times (78)^{2}}{704}$

STEP 8

Calculate the weight range for a height of78 in.
$\text { weight in pounds } = \frac{19 \times (78)^{2}}{704} =148 \, \text{pounds}$ $\text { weight in pounds } = \frac{25 \times (78)^{2}}{704} =196 \, \text{pounds}$ So, the weight range for a healthful BMI for each height is(a)72 in.136 -180 pounds(b)75 in.142 -188 pounds(c)78 in.148 -196 pounds

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QuestionFind the weight range $w$ (to the nearest pound) for a healthful BMI (19-25) at heights: (a) 72 in, (b) 75 in, (c) 78 in using $\mathrm{BMI}=\frac{704 \times(\text { weight })}{(\text { height })^{2}}$ .

Studdy Solution

STEP 1

Assumptions1. The formula for BMI is given by $\mathrm{BMI}=\frac{704 \times(\text { weight in pounds })}{{\text { (height in inches })^{}}^{}}$ . A healthful BMI is between19 and25.
3. We are asked to find the weight range for heights72 in.,75 in., and78 in.

STEP 2

First, we need to rearrange the BMI formula to solve for weight. $\text { weight in pounds } = \frac{\mathrm{BMI} \times (\text { height in inches })^{2}}{704}$

STEP 3

Now, we will use the rearranged formula to find the weight range for a height of72 in. We will do this twice, once for a BMI of19 and once for a BMI of25.
$\text { weight in pounds } = \frac{19 \times (72)^{2}}{704}$ $\text { weight in pounds } = \frac{25 \times (72)^{2}}{704}$

STEP 4

Calculate the weight range for a height of72 in.
$\text { weight in pounds } = \frac{19 \times (72)^{2}}{704} =136 \, \text{pounds}$ $\text { weight in pounds } = \frac{25 \times (72)^{2}}{704} =180 \, \text{pounds}$

STEP 5

Repeat the process for a height of75 in.
$\text { weight in pounds } = \frac{19 \times (75)^{2}}{704}$ $\text { weight in pounds } = \frac{25 \times (75)^{2}}{704}$

STEP 6

Calculate the weight range for a height of75 in.
$\text { weight in pounds } = \frac{19 \times (75)^{2}}{704} =142 \, \text{pounds}$ $\text { weight in pounds } = \frac{25 \times (75)^{2}}{704} =188 \, \text{pounds}$

STEP 7

Repeat the process for a height of78 in.
$\text { weight in pounds } = \frac{19 \times (78)^{2}}{704}$ $\text { weight in pounds } = \frac{25 \times (78)^{2}}{704}$

STEP 8

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QuestionFind the weight range www (to the nearest pound) for a healthful BMI (19-25) at heights: (a) 72 in, (b) 75 in, (c) 78 in using BMI=704×( weight )( height )2 \mathrm{BMI}=\frac{704 \times(\text { weight })}{(\text { height })^{2}} BMI=( height )2704×( weight )​.

Studdy Solution

STEP 1

STEP 2

First, we need to rearrange the BMI formula to solve for weight. weight in pounds =BMI×( height in inches )2704\text { weight in pounds } = \frac{\mathrm{BMI} \times (\text { height in inches })^{2}}{704} weight in pounds =704BMI×( height in inches )2​

STEP 3

STEP 4

STEP 5

Repeat the process for a height of75 in. weight in pounds =19×(75)2704\text { weight in pounds } = \frac{19 \times (75)^{2}}{704} weight in pounds =70419×(75)2​ weight in pounds =25×(75)2704\text { weight in pounds } = \frac{25 \times (75)^{2}}{704} weight in pounds =70425×(75)2​

STEP 6

STEP 7

Repeat the process for a height of78 in. weight in pounds =19×(78)2704\text { weight in pounds } = \frac{19 \times (78)^{2}}{704} weight in pounds =70419×(78)2​ weight in pounds =25×(78)2704\text { weight in pounds } = \frac{25 \times (78)^{2}}{704} weight in pounds =70425×(78)2​

STEP 8

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QuestionFind the weight range $w$ (to the nearest pound) for a healthful BMI (19-25) at heights: (a) 72 in, (b) 75 in, (c) 78 in using $\mathrm{BMI}=\frac{704 \times(\text { weight })}{(\text { height })^{2}}$ .

First, we need to rearrange the BMI formula to solve for weight. $\text { weight in pounds } = \frac{\mathrm{BMI} \times (\text { height in inches })^{2}}{704}$

Repeat the process for a height of75 in.
$\text { weight in pounds } = \frac{19 \times (75)^{2}}{704}$ $\text { weight in pounds } = \frac{25 \times (75)^{2}}{704}$

Repeat the process for a height of78 in.
$\text { weight in pounds } = \frac{19 \times (78)^{2}}{704}$ $\text { weight in pounds } = \frac{25 \times (78)^{2}}{704}$