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Submitted By jacquea1987

Words 764

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Words 764

Pages 4

According to our textbook located on page 151 (Dugopolski, M. (2012) the formula for Body Mass Index (BMI) is: BMI = 703W

H^2

Now, W is equal to an individual’s weight in pounds and H is equal to the height in inches. The height I will be using in the following problems is 70 inches. The stated intervals combine three compound between inequalities, and one “ordinary,” inequality. For the Body Mass Index (BMI) will be used in inequalities; for this formula they will also be supplemented to solve the inequality for W, that will define the ranges of weight that are particular for the height being utilized.

Our first interval indicates which individual might have a longer life span then average. The compound interval that will be used is:

17 < BMI < 22

17 < 703W < 22 Equivalent inequality will be replacing BMI in the formula.

H^2

17 < 703W < 22

(70)^2 I have replaced H^2 with my height in inches.

17 < 703W < 22

4900 We square the denominator and then multiply it by each numerator. In this case it will be 17, 703W, and 22.

17(4900)<703W(4900)<22(4900) It has now been cancelled.

49000

83300<703W<107800 Carry out the multiplication

83300<703W<107800 The terms are then divided by 703 in order to isolate W.

703 703 703

118.5<W<153.3 Those with the height of 70 inches may indeed have a longer than average life span if they weighed in between 118.5 pounds and 153.3 pounds.

In the next inequality problem we will be utilizing a different step-by-step process. However, it will use some of the same work as we did in the first problem. In order to solve our second inequality formula, prior to substituting the height we will find W.

23 < 703W < 25

H^2

23H^2 < 703W < 25H^2 First divide every term by 703 in order to isolate W.

703 703 703

23H^2 < W < 25H^2 With this equivalent inequality we need to solve the 703 703 second weight interval.

23(4900)<W<25(4900)

703 703 The height (squared) is 4900 and is substituted in order to find the second weight interval.

112700<W<122500 Carry out the multiplication.

703 703

160.31<W<174.25 Carry out the division.

Those with the height of 70 inches and weigh between 160.31 pounds and 174.25 pounds are less likely overweight.

The next formula is much more accurate then the first problem we used. We will be using this to find the next two intervals. Our third weight interval will express the range for those that are most likely over weight for this height (70 inches). The values utilized in the compound inequality in place of 23 and 25 are 25 and 30.

25(4900)<W<30(4900) Carry out the multiplication.

703 703

122500<W<147000 703 703 Carry out the division

174.25<W<209.10

Those that are 70 inches and weigh between 174.25 and 209.10 are most likely over weight.

The final weight interval will indicate those that are obese for 70 inches. This is not a compound inequality; so we will only utilize the middle and the right terms of the basic inequality.

W ≥ 30(4900) 703

W ≥147000 Multiplication is carried out. 703

W ≥209.10 Carry out division.

Those that have the height of 70 inches and who weigh more than 209.10 pounds are more than likely obese. In this case they would most likely asset from having and living a healthier life style.

For the following section I will be utilizing those that are least likely not over weight for 70 inches. The terms will be 160.31 and 174.25 pounds. The interval notation will be written as X=(160.31,174.25). We do use parenthesis because “>” and “<” are symbols from an inequality. If we graphed the following terms on a number line it would look like this:

------------------------------------------------ 160.31 174.25

Using the Body Mass Index (BMI) inequality formulas are extremely important when wanting to calculate a more accurate answer. This was very helpful when calculating my own BMI rather than using a chart located in various resources.

Reference

Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY:

McGraw-Hill Publishing.

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