SOLUTION: 3. A chemist mixed a solution that was 34% acid with another solution that was 18% acid to produce a 30 ounce solution that was 28% acid. How much of the 34% acid solution did he u

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Question 1191306: 3. A chemist mixed a solution that was 34% acid with another solution that was 18% acid to produce a 30 ounce solution that was 28% acid. How much of the 34% acid solution did he use?

Answer by math_tutor2020(3817) About Me  (Show Source):
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x = amount of the 34% solution used
y = amount of the 18% solution used
Amounts are in ounces

x+y = 30 ounces total
y = 30-x

34% of x = 0.34x = amount of pure acid from the first solution
18% of y = 0.18y = amount of pure acid from the second solution
0.34x+0.18y = total amount of pure acid

The chemist desires 28% acid solution of the 30 ounce batch, so they want 0.28*30 = 8.4 ounces of pure acid.

0.34x+0.18y = 8.4
0.34x+0.18(30-x) = 8.4 ... replace y with 30-x
0.34x+0.18(30)+0.18(-x) = 8.4
0.34x+5.4-0.18 = 8.4
0.16x+5.4 = 8.4
0.16x = 8.4-5.4
0.16x = 3
x = 3/(0.16)
x = 18.75

Also,
y = 30-x
y = 30-18.75
y = 11.25

The chemist used 18.75 ounces of the 34% solution and 11.25 ounces of the 18% acid solution.