SOLUTION: Hi Tutors: Word problems are powerful they always make me humble. Here goes: A chemist has a solution that is 18%alcohol and one that is 50% alcohol. How many liters of each sho

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Hi Tutors: Word problems are powerful they always make me humble. Here goes: A chemist has a solution that is 18%alcohol and one that is 50% alcohol. How many liters of each sho      Log On

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Question 13778: Hi Tutors:
Word problems are powerful they always make me humble. Here goes:
A chemist has a solution that is 18%alcohol and one that is 50% alcohol. How many liters of each should be mixed together to make 80 liters of a 30% solution? Thank you
SAN ANTONIO
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
First, change the percents to decimals: 18% = 0.18, 50% = 0.5, 30% = 0.3
Now set up the necessary equation. Let x = the number of liters of 18% alcohol solution and (80 - x) = the number of liters of 50% alcohol solution.
%280.18%29x+%2B+%280.5%29%2880+-+x%29+=+%280.3%29%2880%29 Simplify and solve for x.
0.18x+-+0.5x+%2B+40+=+24 Subtract 40 from both sides.
-0.32x+=+-16 Divide both sides by -0.32
x+=+50
The chemist will need 50 liters of the 18% alcohol solution and (80-50=30) 30 liters of the 50% alcohol solution to make 80 liters of 30% alcohol solution.