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# Body mass index Essay

In this assignment I will demonstrate every step of the process of determining my body

mass index or BMI. After finding the body mass index I will then complete the following

intervals based on my height. The formula used to determine the body mass

index is BMI= 703W , where W represents a person weight in pounds and H represents a person
H2

height in inches.

My height is 70 inches. The first interval shows a compound inequality for:

17<BMI<22

17<703W<22
H2To make it an equivalent inequality I replaced the BMI with the formula

17<703W<22
702 My height in inches replaced H2

17<703W<22
4900then multiply by the height that was squared

17(4900)<703W<22(4900)
4900cancelling is performed

83300<703W<107800 multiplication carried out

83300<703W<107800
703 703 703to get W by itself all terms were divided by 703

118.49<W<153.34

After completing the problem I determined that people who are 70 inches may have a longer that average life if they weigh between 118.49 and 153.34

To solve this interval I’m going to solve for W prior to solving the inequality.

23<703W<25
H2 Multiply by H2

23H2<703W<25H2 Divide by 703 to get W by itself

23H2<703W<25H2
703703703 it is now an equivalent inequality

23(4900)<W<25(4900)
703 703from solving the first interval I know that my squared height is 4900. I then plugged it in the place of H2 then multiplied

112700<W<122500
703 703

160.31<W<174 Divide

A person of 70 inches who weighs between 160.31 and 172 is probably not overweight.

The third interval indicates a range for a person that is probably overweight. I solved this

problem by inputting the number into the last compound inequality for 23
& 25.

25<BMI<29.9

25(4900)<W<29.9(4900) Multiply
703 703

122500<W<146510
703 703 Divide

174.25<W<208.41

A person that is 70 inches tall probably is overweight if their weight is between 174.25 and 208.41.

The last interval is to be solved for someone who is obese. The inequality is

BMI≥30 Since this is not a compound inequality I only need to use the middle and right terms.

W≥30(4900) Multiply
703

W≥147000 Divide
703

W≥209.10

This interval indicates a person of 70 inches in height is obese if their weight is greater than or equal to 209.10.

Of the 4 regions I’m going to notate interval 4 which states a person is obese if their

weight is greater than or equal to 209.10.

X is going to represent those who are obese
X= (209.10, ∞)

Graphed it would start at 209.10 pounds and so to infinity or it would never end. —————–(—————————————— 209.10 ∞

In conclusion, during the course of the week I learned two different ways to solve for inequalities. I found that by solving for W in the intervals 2 through 4 was a lot easier and quicker than completing all the steps in the first interval.

Reference
Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing

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