Question

a doctor's prescription for a daily intake of 40 mg of vitamin C and 30 mg of vitamin D your Pharmacy stocks two compounds 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 1

Hi,
Let's say we need x mg from 1st compound, and y mg from 2nd compound.

0.20 × x + 0.40 × y = 40mg
0.30 × x + 0.20 × y = 30mg

0.20(x + 2y) = 40. => x + 2y = 200 => 2y=200-x
0.10(3x +2y) = 30. => 3x + 2y = 300

3x + (200 - x) = 300
2x = 100
x =50mg

50 + 2y = 200
2y = 150
y =75mg