Question

Use a variation model to solve for the unknown value.

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 131-lb person who is 77 in. tall is 15.53. Determine the BMI for an individual who is
76 in. tall and 136 lb.

Answer 1

Let's start by writing the variation equation for BMI:

BMI = k * (weight / height^2)

where k is the constant of variation.

We can use the given information to solve for k:

15.53 = k * (131 / 77^2)

k = 15.53 * 77^2 / 131

k ≈ 6.584

Now we can use this value of k to find the BMI for the second individual:

BMI = 6.584 * (136 / 76^2)

BMI ≈ 20.12

Therefore, the BMI for an individual who is 76 in. tall and 136 lb is approximately 20.12.

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