To solve for the unknown value using a variation model, we start with the formula for Body Mass Index (BMI):
\[ \text{BMI} = k \cdot \frac{W}{H^2} \]
where \( W \) is the weight in pounds, \( H \) is the height in inches, and \( k \) is a constant of proportionality.
Step 1: Find the constant \( k \)
We know the BMI for a 179-lb person who is 68 in tall is 27.21. Plugging these values into the equation:
\[ 27.21 = k \cdot \frac{179}{68^2} \]
Calculating \( 68^2 \):
\[ 68^2 = 4624 \]
Now substitute this into the equation:
\[ 27.21 = k \cdot \frac{179}{4624} \]
To isolate \( k \), we rearrange the equation:
\[ k = 27.21 \cdot \frac{4624}{179} \]
Calculating \( \frac{4624}{179} \):
\[ \frac{4624}{179} \approx 25.8 \]
Now, we multiply:
\[ k \approx 27.21 \cdot 25.8 \approx 702.798 \]
Step 2: Use \( k \) to find the BMI for the 128-lb person who is 60 in tall
Now we use the constant \( k \) to find the BMI for the individual who weighs 128 lb and is 60 in tall.
\[ \text{BMI} = 702.798 \cdot \frac{128}{60^2} \]
Calculating \( 60^2 \):
\[ 60^2 = 3600 \]
Now substitute this back into the equation:
\[ \text{BMI} = 702.798 \cdot \frac{128}{3600} \]
Calculating \( \frac{128}{3600} \):
\[ \frac{128}{3600} \approx 0.03556 \]
Now, substitute this into the equation for BMI:
\[ \text{BMI} \approx 702.798 \cdot 0.03556 \approx 24.96 \]
Conclusion
The body mass index (BMI) for an individual who is 60 inches tall and weighs 128 pounds is approximately:
\[ \text{BMI} \approx 24.96 \]