INTERMEDIATEALGEBRA

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Part(a)

Forthis exercise, Cowlings Rule is used to assist in determining an 11year old child sized dose of 400mg ibuprofen. The formula is a modelas conceptualized by (Dugopolski, 2012) that accurately converts anadult dose in to an adult dose with the child’s age the independentvariable. Literal equations essentially have a single variable butCowling’shas three: a, d and aduly dose (D),

Where

a=“child’s age”

d=“child’s dose”

D= “adult dose”

Theliteral equation is as follows:

d=

Thetask is to calculate an 11 year child’s dose of ibuprofen assumingthat the adult’s dose is 400mg.

RecallingCowlings formula = d=

Wesubstitute known values in the formula. The new literal equationbecomesd=

Calculatingfor the unknown, multiply both sides 24 to reduce the dominator in toa base unit of 1

24d=400 (12)

Theconditional equation as we only have one unknown to make the equationtrue as conceptualized by (Dugopolski,2012).

24d= 4800

Solvingfor d,

d=

Simplifyingthe above equation we get

d=200

Thedose of the 11 year old is 200mg

Part(b)

Thesecond exercise sought to determine a child age given that adultsdose is 1200mg whereas the child’s dose is 400mg child. This taskshall utilize Cowlings Rule whose literal equation is as follows:

d=

Theliteral equation has three variables where:

a=“child’s age”

d=“child’s dose”

D= “adult dose”

Knownvalues are substituted in the formula as follows

400=

Multiplythe right hand side and the left hand side with 24 to eliminate thedenominator

(24)400=1200 (a+1)

Theleft hand side gives 28800

Sincewe have a single element to make the equation true, the conditionalequation becomes since

9600= 1200 (a+1)

Divideboth sides by 1200 to get

8= a+1

Grouplike terms together by subtracting one from both sides

8-1=a

Thereforea =7

Thechild’s age is therefore 7 years of age.

References

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