Elementary and Intermediate Algebra

Read the article about Body Mass Index (BMI) on page 151 of Elementary and Intermediate Algebra. Use the formula given using pounds and inches for finding the BMI at the end of the first paragraph in order to find the four intervals the article mentions:

17 < BMI < 22 might have a longer life span than average

23 < BMI < 25 probably not overweight

25 < BMI < 29.9 probably overweight

BMI > 30 obese
You will use your height to plug into the formula to solve for W, the weight range that will go with each category. You may prefer to solve the formula for the variable W before plugging in values, which is fine.
Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the Instructor Guidance and be concise in your reasoning. In the body of your essay, please make sure to include:

Your solution to the above problem, making sure to include all mathematical work

A discussion on the computed weight ranges and some reasons why they could be misleading

An evaluation of the regions outside of the “probably not overweight” range using both set notation and interval notation. Include a simple graph of the regions. (See Instructor Guidance example for some ideas of how to do this.)

The incorporation of the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; but integrate them into your discussion.):

Inequality

Equivalent

Compound inequality

Interval

My weight is 172 and height is 5 feet 3 inches
Example

INSTRUCTOR GUIDANCE EXAMPLE: Week 2 Written Assignment (paper)
Students, you are perfectly welcome to format your math work just as I have done in these examples. However, the written parts of the assignment MUST be done in your own words. You are NOT to simply copy my wording into your posts!
[The introductory paragraph must be written by each individual student and the content will vary depending on what the student decides to focus on in the general information of the topic.] On page 151 of our textbook we find the formula for Body Mass Index or BMI as
follows:
BMI = 703W H2
Where W = one’s weight in pounds, and Where H = one’s height in inches.
We are asked to calculate four intervals based on our own height. My height is 67.25 inches. The specified intervals include three compound “between” inequalities, and one regular inequality. Everywhere “BMI” shows up in the inequalities I will substitute the formula and solve the inequality for W to specify the weight ranges which fit each category for my height.
The first interval shows who might have a longer life span than average. The compound
inequality for this is:
17 < BMI < 22
17 < 703W < 22 This is an equivalent inequality replacing BMI with the formula. H2
17 < 703W < 22
67.252 H2 has been replaced by my height in inches.
17 < 703W < 22
4522.5625 The next step I multiply all three terms by the denominator.
17(4522.5625) < 703W(4522.5625) < 22(4522.5625) Cancelling is done. 4522.5625
76883.5625 < 703W < 99496.375 The multiplications were carried out.
76883.5625 < 703W < 99496.375 All three terms divided by 703 to isolate W. 703 703 703
109 < W< 141.5
People of height 67.25 inches might have a longer than average life span if they weigh between 109 lbs and 141.5 lbs.
I am now going to do something different. I am going to solve the second inequality formula for W before I plug in the values to find W.

23 < 703W < 25 First, multiply all terms by H2 to take it out of the denominator. H2
23H2 < 703W < 25H2 Divide all terms by 703 to isolate W. 23H2 < W < 25H2
703 703 This is an equivalent inequality to solve for the second weight interval.
I will now plug in my height squared (4522.5625) to find the second weight interval. 23(4522.5625) < W < 25(4522.5625)
703 703 104018.9375 < W < 113064.0625
703 703 148 < W < 161
Multiplication carried out.
Division carried out.
People of height 67.25 inches who weigh between 148 lbs and 161 lbs are probably not overweight.
This method is much more efficient than the first method so I will use it to find the next two intervals as well. The third weight interval indicates the range for probably overweight for this height. I will plug 25.1 and 29.9 into the above compound inequality in place of 23 and 25.
25.1(4522.5625) < W < 29.9(4522.5625) 703 703
113516.31875 < W < 135224.61875 703 703
161.5 < W < 192
Multiplications carried out.
Division carried out
People of height 67.25 inches who weigh between 161.5 and 192 are probably overweight.
The fourth weight interval indicates the range for those who are obese at this height. This is not a compound inequality so I only need to use the middle and right terms of the basic inequality with the opposite pointing arrow and substitute 30 for 29.9.
W = 30(4522.5625)
703
W = 135676.875
703
W = 193
People of height 67.25 inches who weigh 193 or above are most likely obese and would benefit from some serious life-style changes. Although this interval theoretically extends to positive infinity, we know that the weight of a human is eventually self-limiting.
[Student answers to part 3 are going to vary according to their math and understanding of the article.] Multiplication carried out.
Division carried out.
In English I have written the following: People of height 67.25 inches who weigh between 148 lbs and 161 lbs are probably not overweight. In set notation this could be written as follows:
Let X = the set of those who are probably not overweight for the specified height. Then X = {w | w > 148 and w < 161} where w represents the weight of the individual.
In interval notation this would be written as follows: X = (148, 161)
Graphed on a number line this interval could look like this: <————-(———————————-)——————–>
148 161
[The conclusion paragraph must be written by each individual student and the content will vary depending on what the student decides to include in their summary. NOTE: this example does not demonstrate APA format for a paper. The student is responsible for the proper formatting of his or her own work.]