Need help with math, please explain?

Question

Prescribing Drugs.

Doctors often prescribe the same drugs for children as they do for adults. If "a" is the age of a child and "D" is the adult dosage, then to find the child's dosage "d", doctors can use the formula

d = D(a+1)/24 (Cowling's rule) or d = 0.08aD (Fried's rule). For what age do the two formulas give the same child's dosage

Answer 1

given

d=D(a+1)/24

d=0.08aD

Set equations equal to each other, because "d", the child's dosage, is the same (for your question).

D(a+1)/24 = 0.08aD

divide both sides by D

(a+1)/24 = .08a

multiply both sides by 24

(a+1) = 1.92a

1 = .92a

divide both sides by .92

a = 1.09

So the formulas are very close to one another.