The body mass index (BMI) can be expressed with the formula:
\[ \text{BMI} = k \cdot \frac{W}{H^2} \]
where \( W \) is the weight in pounds, \( H \) is the height in inches, and \( k \) is a constant of proportionality.
First, we need to determine the constant \( k \) using the information for the 132-lb person who is 66 inches tall and has a BMI of 21.3.
Given:
- \( W = 132 \)
- \( H = 66 \)
- \( \text{BMI} = 21.3 \)
Plugging these values into the BMI formula, we get:
\[ 21.3 = k \cdot \frac{132}{66^2} \]
Calculating \( 66^2 \):
\[ 66^2 = 4356 \]
Thus, we can rewrite the equation as:
\[ 21.3 = k \cdot \frac{132}{4356} \]
Now, solving for \( k \):
\[ 21.3 = k \cdot \frac{132}{4356} \]
Multiplying both sides by 4356:
\[ 21.3 \cdot 4356 = k \cdot 132 \]
Calculating \( 21.3 \cdot 4356 \):
\[ 21.3 \cdot 4356 \approx 92751.48 \]
Now we can solve for \( k \):
\[ k = \frac{92751.48}{132} \approx 702.6 \]
Now that we have \( k \), we can calculate the BMI for an individual who is 61 inches tall and weighs 158 lb.
Given:
- \( W = 158 \)
- \( H = 61 \)
Using the BMI formula again:
\[ \text{BMI} = k \cdot \frac{W}{H^2} \]
Substituting the values of \( k \), \( W \), and \( H \):
\[ \text{BMI} = 702.6 \cdot \frac{158}{61^2} \]
Calculating \( 61^2 \):
\[ 61^2 = 3721 \]
Now substituting that in:
\[ \text{BMI} = 702.6 \cdot \frac{158}{3721} \]
Calculating \( \frac{158}{3721} \):
\[ \frac{158}{3721} \approx 0.04241 \]
Now we can find the BMI:
\[ \text{BMI} \approx 702.6 \cdot 0.04241 \approx 29.8 \]
Thus, the BMI for an individual who is 61 inches tall and weighs 158 pounds is approximately:
\[ \text{BMI} \approx 29.8 \]
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