SOLUTION: Variation Problem A persons level of fatness is measured using the Body Mass Index, or BMI. A BMI ( rounded to the nearest whole number) in the low 20's is desirable. BMI varies

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Question 180604: Variation Problem
A persons level of fatness is measured using the Body Mass Index, or BMI. A BMI ( rounded to the nearest whole number) in the low 20's is desirable. BMI varies directly a a persons weight in pounds and inversely as the square of the person height in inches. A person who weights 140 pounds and is 70 inches tall has a BMI of 20. Find the BMI of a person who weights 165 pounds and is 71 inches tall.
Answer by Mathtut(3670) About Me  (Show Source):
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Variation Problem
A persons level of fatness is measured using the Body Mass Index, or BMI. A BMI ( rounded to the nearest whole number) in the low 20's is desirable. BMI varies directly a a persons weight in pounds and inversely as the square of the person height in inches. A person who weights 140 pounds and is 70 inches tall has a BMI of 20. Find the BMI of a person who weights 165 pounds and is 71 inches tall.
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direct variation: simply means if one variable rises the other rises and vice versa.
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inverse variation: means if one variable rises the other falls and vice versa
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lets call BMI B
lets call weight W
lets call height H
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BH%5E2%2FW=k where k is the constant of variation
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20%2870%29%5E2%2F140=98000%2F140=700....so k=700
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B%2871%29%5E2%2F165=700.....since H is increasing we would expect that to have a decreasing effect on B. W is increasing and will have an increasing effect on B. H isnt increasing by much but the weight is increasing quite a bit. So I suspect OVERALL this will have an increasing effect on B. Lets find out
:
5041B=700%28165%29 multiplied both sides by 165 to eliminate the fraction and squared the height of 71
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5041B=115500
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highlight%28B=22.91=23%29to the nearest whole. Well there you have it increased just as we visualized.