SOLUTION: A pharmacist has two vitamin-supplement powders. The first powder is 10% vitamin B1 and 30% vitamin B2. The second is 15% vitamin B1 and 20% vitamin B2. How many milligrams of each

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Question 947090: A pharmacist has two vitamin-supplement powders. The first powder is 10% vitamin B1 and 30% vitamin B2. The second is 15% vitamin B1 and 20% vitamin B2. How many milligrams of each powder should the pharmacist use to make a mixture that contains 80 mg of vitamin B1 and 200 mg of vitamin B2?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
x and y for first and second powders

First Powder: 10% B1, 30% B2
Second Powder: 15% B1, 30% B2
Mixture: 80 mg B1, 200 mg B2

Account for B1:
0.1x%2B0.15y=80

Account for B2:
0.3x%2B0.3y=200

Multiply B1 equation by 100 and multiply B2 equation by 10 to form a simplified system
of equations.
system%2810x%2B15y=8000%2C3x%2B3y=2000%29
-
Further simplify the first equation, dividing members by 5.
system%282x%2B3y=1600%2C3x%2B3y=2000%29
You can use any method you know or want for solving the system. Elimination would be
easiest to start with. Just subtract the first equation from the second equation to
eliminate terms of y. Immediatly find:
highlight%28x=400%29, mg of the first powder.
-
3y=1600-2x
y=%281600-2x%29%2F3
y=%281600-2%2A400%29%2F3
highlight%28y=800%29, mg of second powder.