SOLUTION: A doctor's prescription for a daily intake of liquid containing 40 mg of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used. One contains 20% of vi

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A doctor's prescription for a daily intake of liquid containing 40 mg of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used. One contains 20% of vi      Log On


   

Question 373827: A doctor's prescription for a daily intake of liquid containing 40 mg of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used. One contains 20% of vitamin C and 30% vitamin D and the other contains 40% of vitamin C and 20% vitamin D. How many milligrams of each liquid should be mixed to fill the prescription?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = mg of the 1st liquid to be used
Let b = mg of the 2nd liquid to be used
given:
(1) .2a+%2B+.4b+=+40
(2) .3a+%2B+.2b+=+30
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Multiply both sides by 10.
(1) 2a+%2B+4b+=+400
(2) 3a+%2B+2b+=+300
Multiply both sides of (2) by 2
and subtract (1) from (2)
(2) 6a+%2B+4b+=+600
(1) -2a+-4b+=+-400
4a+=+200
a+=+50
and, since
(2) 3a+%2B+2b+=+300
150+%2B+2b+=+300
2b+=+150
b+=+75
50 mg of the 1st liquid and 75 mg of the 2nd liquid
should be used