SOLUTION: A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 35% and the third contains 75%. He wants to use all three solutions to

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Question 793645: A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 35% and the third contains 75%. He wants to use all three solutions to obtain a mixture of 64 liters containing 55% acid, using 3 times as much of the 75% solution as the 35% solution. How many liters of each solution should be used?
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x = liters of 25%
y = liters of 35%
z = liters of 75%
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Restriction given, z=3y. We can rewrite the variable assignments:
x = liters of 25%
y = liters of 35%
3y = liters of 75%

Account for concentration of the intended acid solution:
%2825x%2B35y%2B3y%2A75%29%2F64=55
and simplify,
%2825x%2B%2835%2B3%2A75%29y%29%2F64=55
%2825x%2B260y%29%2F64=55
25x%2B260y=64%2A55
5x%2B52y=64%2A11
5x%2B52y=704

Account for volume:
x%2By%2B3y=64
x%2B4y=64

Work with the system of the two equations in x and y:
highlight%285x%2B52y=704%29
highlight%28x%2B4y=64%29
Once x and y solved, you can compute z.

The steps from here are not provided but are omitted intending for you to do them. Tell me if this is troublesome. Analyzing the problem and coming up with the system of equations is the hardest and most important part.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 35% and the third contains 75%. He wants to use all three solutions to obtain a mixture of 64 liters containing 55% acid, using 3 times as much of the 75% solution as the 35% solution. How many liters of each solution should be used?
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Equation:
acid + acid + acid = acid
x + y + z = 64
0.25x + 0.35y + 0.75z = 0.55*64
z = 3y
=========================
x + y + 3y = 64
0.25x + 0.35y + 0.75(3y) = 0.55*64
=============================
x + 4y = 64
0.25x + 2.6y = 35.2
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25x + 100y = 1600
25x + 260y = 3520
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Solve for "y":
160y = 1920
y = 12 liters (amt. of 35% solution needed)
x = 3y = 36 liters (amt. of 25% solution needed)
z = 64-12-36 = 16 liters (amt. of 75% solution needed)
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Cheers,
Stan H.
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