The Calculation of BMI

Introduction to algebra

Body mass index is a figure that is used to provide an estimate about a person’s weight in relation to that used in describing obesity. It is basically a ratio of one’s weight to their height.

In our context, the unit of measurement for weight is pounds while height is measured in inches.

The formula for this figure is weight in pounds divided by the square of the height in inches which is then multiplied by a factor of 703.

BMI= Weight (lbs) / [Height (in)]^{2}* 703

BMI= W /H^{2 }* 703

Since my height at present is 5feet, five inches, I can use the formulae provided to estimate my recommended weight as well as which weight is obese and also which one is underweight.

For this weight to be calculated efficiently, the formula will need to be in such a manner that all the knowns are on one side and the unknown (my weight) on the other side.

To eliminate the fraction, every element will have to be multiplied by the denominator which is H^{2}.

H^{2 }*BMI= H^{2 }*[(W /H^{2 }) * 703] which is a **complex inequality**

(H^{2 }*BMI) = (W * 703)]

At this stage, we can place W on one side of the equation and all the other variables on the other.

(H^{2 }*BMI) * 1/703= (W * 703)] * 1/703

This leaves us with: W = H^{2 }*BMI/703 in which weight is **equivalent**to the product of height squared and BMI divided by the factor of 703

If the height is 5 ft. 5 inches and one foot is 12 inches, then the height in inches is 65 inches

Therefore H = 65.

This new formula of *W = H ^{2 }*BMI/703*can be then applied to the ranges given for BMI.

For the **inequality **17 < BMI < 22 I might have a longer life span than average

If BMI = 17,

W= (65^{2 }* 17)/ 703

W= 102.2 lb

If BMI = 22,

W= (65^{2 }* 22)/ 703

W= 132.22 lb

If my weight is between the **interval of **102.2 lb. and 132.2 lb. , I might live longer

For the **inequality **23< BMI < 25 I am probably not overweight

If BMI = 23,

W= (65^{2 }* 23)/ 703

W= 138.23lb

If BMI = 25,

W= (65^{2 }* 25)/ 703

W= 150.25lb

If my weight falls between the **interval of** 138.2 lb. and 150.25 lb. I am probably not overweight

For the **inequality 25**< BMI < 29.9 I am probably overweight

If BMI = 25,

W= (65^{2 }* 25)/ 703

W= 150.25 lb

If BMI = 29.9,

W= (65^{2 }* 29.9)/ 703

W= 179.7 lb

If my weight is between the **interval of **150.25 lb. and 179.7 lb. then I am probably overweight

BMI > 30 obese

If BMI = 30

W= (65^{2 }* 30)/ 703

W= 180.3 lb.

If my weight is at 180.3 and above, I am definitely obese. Basically from the figure of 180.3 up to **infinity** the verdict will remain obesity.

A table of weight and the respective BMI and a graph of the same

Weight | BMI |

132 | 17 |

138 | 23 |

150 | 25 |

180 | 30 |

Though helpful, the BMI is not an accurate measure of body fat since at times one could have a high reading due to his or her heavy muscle build such as athletes. Women, at the same BMI as men have been found to have higher body fat amounts. Another factor that affects the level of body fat is age. The implications of BMI are interpreted differently depending on the age of the person.

References

Class Text: Elementary and Intermediate Algebrapp 151

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