# Inequalities: Body Mass Index and Compound Inequality

Inequalities

Deborah White

Ashford University

MAT221: Introduction to Algebra (AFN1312A)

Instructor: Tracy Abram

April 1, 2013

On page 151 of Elementary and Intermediate Algebra, the Body Mass Index (BMI) is given as: BMI= 703W/H2

W = one’s weight in pounds

H = one’s height in inches.

By calculating four intervals based on your height can be possible by using the Body Mass Index formula. However, in this situation I am going to use inequalities to calculate Body Mass Index(BMI) which is meant to use my height to calculate if I’m overweight , having a longer life span than average, or to calculate if I’m obese. In the real world it is significant to have knowledge about being overweight because this could come into the use of attention of medical assistance. By using inequalities and solving them could serve a far more severe importance than just a mathematical problem. The first interval for this problem is the solvation for a longer life span than average. 17< BMI <22The compound inequality.

17< 703W/H2 <22Use the BMI formula in replace of the original compound inequality so we now have an equivalent inequality.

17< 703W/62.002 <22 I replaced H2 for my height in inches. 17< 703W/3844 <22Then, I multiplied the three numbers by the denominator to rid the

exponent that was on the bottom associated with my height. 17(3844)< 703W(3844)/3844 < 22(3844) In the fraction bar, the cancelling is made. 65348< 703W< 84568 The multiplications were carried out when I multiplied all of the

numbers by 32844.

65348/703 < 703W/703 < 84568/703 I divide all three of the fractions by 703 to get W by itself. 93< W< 120.3

People who have the height of 62 inches will have a longer life span between the weight of 93 and 120.3 pounds. For my second interval, there are two ways of solving it. Without solving for W at the end, I’m going to separate W by itself before I go about solving it. 23<...

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