# Solving systems of linear equations

• Apr 27th 2009, 07:56 PM
vidalex
Solving systems of linear equations
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?

I know the answer is 1.1, but I don't know how to get to this answer not using a graphing calculator.
• Apr 27th 2009, 09:18 PM
SengNee
Quote:

Originally Posted by vidalex
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?

I know the answer is 1.1, but I don't know how to get to this answer not using a graphing calculator.

Cowling's rule:
$d_c=\frac{D(a+1)}{24}$

Fried's rule:
$d_f=0.08aD$

Given, the same child's dosage

Therefore, $d_c=d_f$
• Apr 28th 2009, 06:33 AM
stapel
Quote:

Originally Posted by vidalex
...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?

I know the answer is 1.1, but I don't know how to get to this answer....

Since each is equal to "d" and since you need to find the age "a", then set them equal:

. . . . .[D(a + 1)]/24 = 0.08aD

You can start the solution by dividing through by D. Then solve the resulting linear equation by whatever methods they have taught you. (Wink)