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 179-lb person who is 68 in, tall is 27.21. Determine the BMI for an individual who is 60 in, tall and 128 lb.

1 answer

To solve for the unknown value using a variation model, we start with the formula for Body Mass Index (BMI):

BMI=kWH2

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=k179682

Calculating 682:

682=4624

Now substitute this into the equation:

27.21=k1794624

To isolate k, we rearrange the equation:

k=27.214624179

Calculating 4624179:

462417925.8

Now, we multiply:

k27.2125.8702.798

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.

BMI=702.798128602

Calculating 602:

602=3600

Now substitute this back into the equation:

BMI=702.7981283600

Calculating 1283600:

12836000.03556

Now, substitute this into the equation for BMI:

BMI702.7980.0355624.96

Conclusion

The body mass index (BMI) for an individual who is 60 inches tall and weighs 128 pounds is approximately:

BMI24.96

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