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

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Mathematics

Kendall Humphrey

2 March, 21:54

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

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Roberto Downs · 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