Kayla R.

asked • 10/10/16

Math question

pire acid is to be added to 5% acid solution to obtain 95l of 40% solution. What amounts of each should be used?
how many of 100% pure acid should be used to make the solution? 
 
How many liters of the 5% solution should be in the mixture?

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Mark M. answered • 10/10/16

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x represents the amount of pure acid
0.05(95) + 1.00x = 0.40(95 + x)
 
Can you solve for x?
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CAROLYN H.

Using your equation you get 0.6x = 33.25 or x = 665/12.  However, 0.05(95) + (1-.05)x = 0.40(95) does work and gives the result of x = 35.  35 liters of pure acid added to 3 liters (60 liters x 0.05) from the 5% solution = 38 liters (95 liters x 0.40) of the final solution.
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10/10/16

Mark M.

If x represents the amount of pure acid, why is it 95% rather than 100%?
If x amount of pure acid is added, wouldn't the result be 95 + x?
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10/10/16

CAROLYN H.

The question stated "pire acid is to be added to 5% acid solution to obtain 95l of 40% solution." The final solution amount is 95 liters. x amount of pure acid is added to a quantity y of 5% solution to produce an end result of 95 liters of 40% final solution. x+y = 95. The amount of acid in the final solution is 38 liters (.40x95) - the rest is water. 35 liters of that acid comes from the pure substance x and 3 liters of that acid comes from the 5% solution (0.05x60 liters).
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10/11/16

CAROLYN H. answered • 10/10/16

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X= liters of 100% (pure acid), Y = liters of 5%
First Equation is    X+Y = 95 liters
Second Equation is    (1)X + 0.05Y = (0.40)(95) = 38  so  Substitute Y = 95-X (First EQ) into second EQ
and   X + 0.05(95-X) = 38; X + 4.75 - 0.05X = 0.95X + 4.75 = 38; 0.95X = 33.25; X = 35; Y = 60
You need 35 liters of pure acid to be mixed with 60 liters of the 5% solution to get 95 liters of 40% solution
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CAROLYN H.

35 liters of pure acid added to 3 liters (60 liters x 0.05) of the 5% solution = 38 liters (95 liters x 0.40) of the final solution.
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10/10/16

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