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Question

a doctors prescription calls for the creation of pills that contain 20 units of vitamin B12 and 12 units of vitamin E. Your pharmacy stocks two powders that can be used to make these pills. One contains 20% vitamin B12 and 40% vitamin E the other containa 50% vitamin B12 and 30% vitamin E. How many units of each powder should be mixed in each pill.

Answer 1

Let X = units of powder with 20% B12 and 40% E

Let Y = units of powder with 50% B12 and 30% E 

 

In a mixture of X units of powder 1 and Y units of powder 2 there will be 

 

0.20*X + 0.50*Y units of B12

0.40*X + 0.30*Y units of E 

 

We want the 1st equation to equal 20 and the 2nd equation to equal 12 

 

0.20*X + 0.50*Y = 20

0.40*X + 0.30*Y = 12

 

Multiply the 1st equation by (-2) and then add the 2 equations together 

 

-0.40*X - 1.00*Y = -40

 0.40*X + 0.30*Y = 12

 

-0.70*Y = -28

Y = 40

 

Plug this value for Y into the 1st equation 

 

0.20*X + 0.50*(40) = 20

0.20*X + 20 = 20

0.20*X = 0

X = 0 

 

There should be 0 units of powder 1 (20% B12 and 40% E) mixed with 40 units of powder 2 (50% B12 and 30% E) in each pill.  

 

Check:  0*0.20 + 40*0.50 = 0 + 20 = 20 units of B12

            0*0.50 + 40*0.30 = 0 + 12 = 12 units of E