Chapter 11.1, Problem 67AYU

Pharmacy A doctor’s prescription calls for a daily intake containing 40 milligrams (mg) of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used: One contains $20\%$ vitamin C and $30\%$ vitamin D. the other $40\%$ vitamin C and $20\%$ vitamin D. How many milligrams of each compound should be mixed to fill the prescription?

To determine

To find: A doctor’s prescription calls for a daily intake containing 40 milligrams (mg) of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used: One contains $20\%$ vitamin C and $30\%$ vitamin D, the other $40\%$ vitamin C and $20\%$ vitamin D. How many milligrams of each compound should be mixed to fill the prescription?

Answer to Problem 67AYU

50mg of first compound and 75 mg of second compound should be used.

Explanation of Solution

Given:

A doctor’s prescription calls for a daily intake containing 40 milligrams (mg) of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used: One contains $20\%$ vitamin C and $30\%$ vitamin D, the other $40\%$ vitamin C and $20\%$ vitamin D.

Calculation:

Let $a$ be the mg of the first liquid to be used and $b$ be mg of the second liquid to be used.

$.2a+.4b=40$   -----1

$.3a+.2b=30$   -----2

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

$2a+4b=400$   -----1

$3a+2b=300$   -----2

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

$6a+4b=600$   -----3

Subtracting equation 3 from equation 1 we have,

$4a=200$

$a=50$

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

$3a+2b=300$   -----2

$150+2b=300$

$b=75$

Therefore, 50mg of first compound and 75 mg of second compound should be used.