Q. 68 - Precalculus Enhanced with Graphing Utilities

Question

A doctor’s prescription calls for the creation

of pills that contain 12 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 30% vitamin E, the other 40% vitamin B12 and 20% vitamin E. How many units of each powder should be mixed in each pill?

Step-by-Step Solution

Answer

30 units of b12 powder and 15 units of vitamin E powder.

Step 1: Given information

Your pharmacy stocks two powders that  can be used to make these pills: one contains 20% vitamin B12 and 30% vitamin E, the other 40% vitamin B12 and 20% vitamin E.

Step 2: Find the equations

let x be the mass of first compound and y be the mass of second compound

one contains 20% vitamin B12 and 30% vitamin E, 

Hence 

$$\begin{gathered} 0.2x+0.4y=12 \\ 2x+4y=120 \left(1\right) \end{gathered}$$

The other 40% vitamin B12 and 20% vitamin E.

$$\begin{gathered} 0.3x+0.2y=12 \\ 3x+2y=120 \left(2\right) \end{gathered}$$

Step 3: Solve the equation

To solve the equation we multiply equation 2 by 2 and subtract from equation from 1

We get

$2x+4y=120-6x-4y=-240-4x=-120$

Therefore, $x=30$

Now we find the value of y

$$\begin{gathered} 2x+4y=120 \\ 2\left(30\right)+4y=120 \\ 4y=60 \\ y=15 \end{gathered}$$

Step 4: Conclusion

30 units of b12 powder and 15 units of vitamin E powder.