The body mass index, I, can be used to determine an individual’s risk for heart

Question

The body mass index, I, can be used to determine an individual’s risk for heart disease. An index less than 25 indicates a low risk. The body mass index is given by the formula, or model. I=700W/H2, where W=weight, in pounds, and H=height, in inches. Francis weighs 213 pounds and stands 70 inches tall. What is his approximate body mass index? Find an inequality describing all weights W that Francis can have and be in the lowrisk category.

1. approximate body mass index is?
2. show an inequality describing all weights W in the low risk category.

Explanation / Answer

1. Plugging in the values of Francis' weight and height into the formula for Body Mass Index, we find that I=700(213)/702, which approxamitely equals 30.43 for Francis' BMI.

2. Now since we know that Francis is 70 inches tall, we can plug in 70 right away into the equation to get I=700W/702, and after we reduce this we get I=W/7 for Francis' BMI in terms of his weight. Now since we want the BMI to be less than 25, we can write I<25 to start our inequality. Then, replacing I with W/7, we find that (W/7)<25, or if we multiply both sides by 7 we get W<175. So as long as Francis weighs less than 175 pounds, he will be in the low risk category.

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