Chapter 11.1, Problem 68AYU

Pharmacy A doctor’s prescription calls for the creation of pills that contain 12 units of vitamin $B_{12}$ and 12 units of vitamin E. Your pharmacy stocks two powders that can be used to make these pills: One contains $20\%$ vitamin $B_1{}_2$ and $30\%$ vitamin E, the other $40\%$ vitamin $B_{12}$ and $20\%$ vitamin E. How many units of each powder should be mixed in each pill?

To determine

To find: 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?

Answer to Problem 68AYU

30 units of one powder and 15 units of another powder to be mixed in each pill.

Explanation of Solution

Given:

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.

Calculation:

Let one powder be $a$ and another powder be $b$.

$.2a+.4b=12$   -----1

$.3a+.2b=12$   -----2

Multiplying by 10 on both sides of equation $1\&2$ we have,

$2a+4b=120$   -----1

$3a+2b=120$   -----2

Multiplying by 2 on both sides of equation 2 we have,

$6a+4b=240$   -----3

Subtracting equation 3 from equation 1 we have,

$4a=120$

$a=30$

Using the value of $a$ to find $b$ using equation 2, we have,

$3a+2b=120$   -----2

$90+2b=120$

$b=15$

Therefore, 30 units of one powder and 15 units of another powder to be mixed in each pill.