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 801751: 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 70 mg of vitamin B1 and 180 mg of vitamin B2?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = how many mg. of the first powder.
Let y = how many mg. the second powder.

Accounting for vB1, 0.10x%2B0.15y=70
Accounting for vB2, 0.30x%2B0.20y=180
Look carefully how the units work to see that these equations make sense. The accountings are for milligrams of each B vitamin.

Simplify the system, multiplying each equation by only 10:
x%2B%283%2F2%29y=700 and 3x%2B2y=1800
Integer coefficients would be more comfortable, so maybe try multiply the first equation by 2:
2x%2B3y=1400 and 3x%2B2y=1800
Substitution seems like might be easier than trying elimination, so,


2x=1400-3y
x=700-%283%2F2%29y
substitute into the other equation,
3%28700-%283%2F2%29y%29%2B2y=1800
2100-%289%2F2%29y%2B2y=1800
2100-1800=%289%2F2%29y-2y
%289%2F2-4%2F2%29y=300
%285%2F2%29y=300
y=300%282%2F5%29=highlight%28120%29 milligrams of the second powder. Use any formula to find value for x.