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# System of Equations

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?

### 1 Answer by Expert Tutors

Dattaprabhakar G. | Expert Tutor for Stat and Math at all levelsExpert Tutor for Stat and Math at all le...
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Joey:

One unit of D1 contains 1 mg of X and 2 mg of Y.  One unit of D2 contains 2 mg of X and 3 mg of Y

Suppose you choose a units of D1 and b units of D2.  Then you get a mg of X and 2a mg of Y (from D1) and 2b mg of X and 3b mg of Y from D2.  So you get a total of a + 2b  mg of X and 2a + 2b mg of Y.  What you want is

a + 2b = 13

2a + 3b  = 22

Multiply first equation by 2 throughout:  2a + 4b = 26.  Subtract the second equation to get b = 4.  That gives a + 8 = 13, so that a = 5.

Answer: Take 5 units of D1 and 4 units of D2.  Check for yourself that you get 13 mg of X and 22 mg of Y, total, by doing so.  (I have!)

Dattaprabhakar (Dr. G.)