Discussion: Formulas
•
•
Read about Cowling`s Rule for child sized doses of medication (number 92 on page 119 of
Elementary and Intermediate Algebra).
Solve parts (a) and (b) of the problem using the following details indicated for the first letter of
your last name: ( Use my last name Griffin).
If your last name starts with
letters
For part (a) of problem 92 use
this information to calculate the
child`s dose.
For part (b) of the problem 92
use this information to calculate
the child`s age.
A or Z
Adult dose 400mg ibuprofen; 5
year old child
Adult dose 500mg amoxicillin; 11
year old child
Adult dose 1000mg
acetaminophen; 8 year old child
Adult dose 75mg Tamiflu; 6 year
old child
Adult dose 400mg ibuprofen; 7
year old child
Adult dose 500mg amoxicillin; 9
year old child
Adult dose 1000mg
acetaminophen; 6 year old child
Adult dose 75mg Tamiflu; 11
year old child
Adult dose 400mg ibuprofen; 8
year old child
Adult dose 500mg amoxicillin; 4
year old child
800mg adult, 233mg child
Adult dose 1000mg
acetaminophen; 3 year old child
Adult dose 75mg Tamiflu; 5 year
old child
75mg adult, 12.5mg child
C or X
E or V
G or T
I or R
K or P
M or N
O or L
Q or J
S or H
U or F
W or D
250mg adult, 52mg child
600mg adult, 250mg child
500mg adult, 187mg child
1200mg adult, 200mg child
100mg adult, 12.5mg child
600mg adult, 200mg child
1000mg adult, 600mg child
500mg adult, 250mg child
300mg adult, 100mg child
1200mg adult, 300mg child
Y or B
•
•
Adult dose 400mg ibuprofen; 2
year old child
400mg adult, 50mg child
Explain what the variables in the formula represent and show all steps in the computations.
Incorporate 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; use them
appropriately in sentences describing your math work.)
o
o
o
o
o
Literal equation
Formula
Solve
Substitute
Conditional equation
Your initial post should be 150- 250 words in length. No plagiarism and read directions carefully.
Running Head: INEQUALITIES
1
Running head should use a shortened version of the title if the title is long! All capital
letters for the title and the words Running and Head should be capitalized as well.
Inequalities (full title; centered horizontally & vertically)
First Name Last Name
MAT 221
Dr. XXXXXXX XXXXXXXX
Date
INEQUALITIES
2
Inequalities
Be sure to have a centered title on page 1 of your papers!!
[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. YOUR
INTRODUCTION SHOULD CONNECT MATH CONCEPTS AND REAL-WORLD
APPLICATIONS. DO NOT INCLUDE THE DIRECTIONS IN THE INTRO! The following
paragraph is not an introduction to the paper but rather the beginning of the assignment.]
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!
On page 151 of the textbook (Dugopolski, 2012) is the formula for Body Mass Index or
BMI as follows: BMI = 703W
H2
Where W = one’s weight in pounds, and H = one’s height in inches.
Using personal height, four intervals must be found using compound inequalities. The
height used in these problems is 67.25 inches. The specified intervals include three compound
“between” inequalities and one regular inequality. Body Mass Index, or BMI, shows up in the
inequalities and this formula will be substituted to solve the inequality for W to specify the
weight ranges that fit each category for the height being used.
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
(67.25)2
H2 has been replaced by the height in inches.
INEQUALITIES
3
17 < 703W < 22
4522.5625
The denominator was square and then multiplied times
each term in the numerator: 17, 703W, and 22.
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
This solution shows the range for weight.
People of height 67.25 inches might have a longer than average life span if they weigh between
109 lbs. and 141.5 lbs.
In the next problem, a different process will be used since the first problem includes some
of the same work. To solve the second inequality formula, a solution for W will be found prior
to substituting in the height.
23 < 703W < 25
First, multiply all terms by H2 to take it out of the denominator.
H2
23H2 < 703W < 25H2
703
703
Divide all terms by 703 to isolate W.
703
23H2 < W < 25H2
This is an equivalent inequality to solve for the second
703
weight interval. The height squared (4522.5625) is substituted into
703
the formula find the second weight interval.
23(4522.5625) < W < 25(4522.5625)
703
703
INEQUALITIES
4
104018.9375 < W < 113064.0625
703
Multiplication carried out.
703
148 < W < 161
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 it will be used to find the
next two intervals as well. The third weight interval indicates the range for probably overweight
for this height. Values substituted into the above compound inequality in place of 23 and 25 are
25.1 and 29.9.
25.1(4522.5625) < W < 29.9(4522.5625)
703
703
113516.31875 < W < 135224.61875
703
Multiplications carried out.
703
161.5 < W < 192
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 only the middle and right terms of the basic inequality are
used with the opposite pointing arrow and substitute 30 for 29.9.
W ≥ 30(4522.5625)
703
W ≥ 135676.875
703
W ≥ 193 Division carried out.
Multiplication carried out.
INEQUALITIES
5
People of height 67.25 inches who weigh 193 lbs. or above are most likely obese and would
benefit from some serious life-style changes. Although this interval theoretically extends to
positive infinity, 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.]
In English the following was written: 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.
Because the weight is between 148 and 161, “w” has to be larger than the smallest number (148)
and smaller than the larger number (161).
In interval notation this would be written as follows: X = (148, 161) Parentheses are used
because of the > and < symbols from the inequality. This demonstrates neither number is
included in the solution set.
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. DO NOT INCLUDE
PERSONAL NARRATIVE LIKE “I LEARNED…” OR “WE CAN DO….”. BE SURE TO
SUMMARIZE WHY THE CONCEPT(S) ARE IMPORTANT AND HOW THEY CAN BE
CONNECTED TO OTHER CONCEPTS.]
INEQUALITIES
6
Reference
Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY:
McGraw-Hill Publishing.
Use the word ‘Reference’ or ‘References’ as the title. THERE IS NO COLON OR
UNDERLINE.
Textbook should ALWAYS be included in every assignment! Be sure to use appropriate
indentation (hanging), font (Arial or Times New Roman), and size (12).
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