The body mass index (BMI) of an individual varies directly as the weight of the individual and inversely as the square of the height of the individual. The body mass index for a 179-ib person who is 70 in. tall is 25.68. Determine the BMI for an individual who is 71 in. tall and 176 lb.

Answer 1

The Body Mass Index (BMI) can be expressed with the formula:

\[ \text{BMI} = k \cdot \frac{W}{H^2} \]

where \(W\) is the weight of the individual, \(H\) is the height, and \(k\) is a constant of proportionality.

Given the information for the first individual:

• Weight (\(W_1\)) = 179 lb
• Height (\(H_1\)) = 70 in
• BMI = 25.68

We can rearrange the formula to solve for \(k\):

\[ 25.68 = k \cdot \frac{179}{70^2} \]

Calculating \(70^2\):

\[ 70^2 = 4900 \]

Substituting this value into the equation:

\[ 25.68 = k \cdot \frac{179}{4900} \]

Now, we can solve for \(k\):

\[ k = 25.68 \cdot \frac{4900}{179} \]

Calculating \( \frac{4900}{179} \):

\[ \frac{4900}{179} \approx 27.3855 \]

Now calculating \(k\):

\[ k \approx 25.68 \cdot 27.3855 \approx 703.82 \]

Now that we have \(k\), we can find the BMI for the second individual who is:

• Weight (\(W_2\)) = 176 lb
• Height (\(H_2\)) = 71 in

Using the BMI formula:

\[ \text{BMI}_2 = k \cdot \frac{W_2}{H_2^2} \]

Calculating \(H_2^2\):

\[ 71^2 = 5041 \]

We can now calculate the BMI:

\[ \text{BMI}_2 = 703.82 \cdot \frac{176}{5041} \]

Calculating \( \frac{176}{5041} \):

\[ \frac{176}{5041} \approx 0.03488 \]

Now substitute this back into the BMI formula:

\[ \text{BMI}_2 \approx 703.82 \cdot 0.03488 \approx 24.5 \]

Thus, the BMI of the individual who is 71 inches tall and weighs 176 pounds is approximately 24.5.