If a doctor uses Cowling's rule to prescribe 187 milligrams of Tamiflu to a child when she would prescribe 500 milligrams to an adult, then how old is the child?
Cowling's Rule
d=D(a+1)/24
d = 187
D = 500
Solve for a.
To determine the age of the child, we can use Cowling's rule as mentioned in the question. Cowling's rule is a method used to calculate pediatric drug dosages based on the dosage prescribed for adults. According to Cowling's rule, the dosage for a child is calculated by multiplying the adult dosage by the child's age in years divided by the sum of the child's age in years and 12.
Let's use this method to find the age of the child:
Given:
Adult dosage = 500 milligrams (mg)
Child dosage = 187 milligrams (mg)
Using Cowling's rule, we have the equation:
Child dosage = Adult dosage * (Child's age / (Child's age + 12))
Substituting the given values into the equation:
187 mg = 500 mg * (Child's age / (Child's age + 12))
To solve for the child's age, we can cross-multiply:
187 mg * (Child's age + 12) = 500 mg * Child's age
Distributing the multiplication:
187 mg * Child's age + 187 mg * 12 = 500 mg * Child's age
Simplifying the equation:
187 mg * Child's age + 2244 mg = 500 mg * Child's age
Rearranging the equation to isolate the child's age:
500 mg * Child's age - 187 mg * Child's age = 2244 mg
313 mg * Child's age = 2244 mg
Child's age = 2244 mg / 313 mg
Calculating:
Child's age = 7.17 years
Therefore, based on Cowling's rule, the child is approximately 7.17 years old.