SOLUTION: A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 40% and the third contains 85% . He wants to use all three solutions to

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 40% and the third contains 85% . He wants to use all three solutions to      Log On


   

Question 1077881: A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 40% and the third contains 85% . He wants to use all three solutions to obtain a mixture of 108 liters containing 45% acid, using 2 times as much of the 85% solution as the 40% solution. How many liters of each solution should be used?
The chemist should use _____ liters of 25% solution, _____ liters of 35% solution, and ____ liters of 75% solution.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The first acid solution contains 25% acid, the second contains 40% and the third contains 85% . He wants to use all three solutions to obtain a mixture of 108 liters containing 45% acid, using 2 times as much of the 85% solution as the 40% solution. How many liters of each solution should be used?
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x of 25%
y of 40%
z of 85%
z%2Fy=2

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Account for the pure acid
25x%2B40y%2B85%2A2y=108%2A45
5x%2B8y%2B17%2A2y=108%2A9
5x%2B8y%2B34y=972
5x%2B42y=972

Account for the volume
x%2By%2B2y=108
x%2B3y=108

Simpler system in two variables: system%285x%2B42y=972%2Cx%2B3y=108%29
Use five times the second equation and subtract from first equation.

5x%2B42y-5x-15y=972-540
42y-15y=432
27y=432
highlight%28y=16%29

highlight%28x=60%29

highlight%28z=32%29

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60 liters of 25%
16 liters of 40%
32 liters of 85%