The treatment of a certain viral disease requires a combination dose of drugs D1 and D2. Each unit of D1 contains 1 milligram of factor X and 2 milligrams of factor Y, and each unit of D2 contains 2 milligrams of factor X and 3 milligrams of factor Y. If the most effective treatment requires 13 milligrams of factor X and 22 milligrams of factor Y, how many units of D1 and D2 should be administered to the patient.

Question

I know that I have to form at least two equations from this problem because I have to use the substitution or elimination method to solve this problem. I know that the answers are: D1=5 and D2=4 but I don't know what equations to form and what to substitute or eliminate

Answer 1

Let G be the number of "Units" of D1 and H be the number of un its of D2.
The equations you have to satisfy are:
G + 2H = 13(the amount of drug X needed)
2G + 3H = 22 (the amount of drug Y needed).
2G + 4H = 26
H = 4
G = 13 - 8 = 5