SOLUTION: A Pharmacist needs 500 ml of 10% phenobarbital solution. She has only a 5% phenobarbital solution and a 25% phenobarbital solution available. How many ml of 5% solution should she

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A Pharmacist needs 500 ml of 10% phenobarbital solution. She has only a 5% phenobarbital solution and a 25% phenobarbital solution available. How many ml of 5% solution should she       Log On


   

Question 1198982: A Pharmacist needs 500 ml of 10% phenobarbital solution. She has only a 5% phenobarbital solution and a 25% phenobarbital solution available. How many ml of 5% solution should she mix to obtain the desired solution.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
SOLUTION CONC. %        VOL.mL       PURE
         5                x          0.05x
        25              500-x        0.25(500-x)
        10              500          0.10*500

0.05x%2B0.25%28500-x%29=0.10%2A500--------solve this equation for x.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If a formal algebraic solution is not required, here is a quick and easy way to solve any 2-part mixture problem like this.

Look at the three percentages 5, 10, and 25 on a number line and observe/calculate that 10% is 5/20 = 1/4 of the way from 5% to 25%. That means 1/4 of the mixture has to be the 25% solution.

1/4 of 500 ml is 125 ml, so the mixture needs to be 125 ml of the 25% solution and 375 ml of the 5% solution.

ANSWER: He needs 375 ml of the 5% solution.