SOLUTION: Bill Bilderback, a druggist, needs 1000 milliliters of a 10% phenobarbital solution. He has only 5% and 25% phenobarbital solution available. How many milliliters of each solutio

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Question 18703: Bill Bilderback, a druggist, needs 1000 milliliters of a 10% phenobarbital solution. He has only 5% and 25% phenobarbital solution available. How many milliliters of each solution should he mix to obtain the desired solution?
I'm also supposed to put this in a linear systems form, if that makes sense. Thank you for your help.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Bill needs to add x ml. of 5% phenobarbital solution to (1000-x) ml. of 25% phenobarbital solution to make 1,000 ml. of 10% phenobarbital solution.
After changing the percents to their decimal equivalents, write the linear equation from the problem description.
0.05x+%2B+0.25%281000-x%29+=+0.1%281000%29 Simplify and solve for x.
0.05x+%2B+250+-+0.25x+=+100 Combine like-terms.
-0.2x+%2B+250+=+100 Add 0.2x to both sides.
250+=+100+%2B+0.2x Subtract 100 from both sides.
150+=+0.2x Divide both sides by 0.2
x+=+750
Bill will need to mix 750 ml. of 5% phenobarbital solution with (1000-750) = 250 ml. of 25% phenobarbital solution to obtain 1,000 ml. of 10% phenobarbital solution.