Answers:
170 mL of the 10% solution
30 mL of the 60% solution
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Work Shown
Label the two inputs as A and B
A: 10% acid
B: 60% acid
x = amount of A
200-x = amount of B
0.10x = amount of pure acid from A
0.60(200-x) = amount of pure acid from B
The goal is to have 200 mL of a 17.5% solution, so we want to have 200*0.175 = 35 mL of pure acid after mixing batches A and B.
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0.10x + 0.60(200-x) = 35
0.10x + 120 - 0.60x = 35
-0.50x + 120 = 35
-0.50x = 35-120
-0.50x = -85
x = -85/(-0.50)
x = 170 mL is the amount of the 10% acid solution
200-x = 200-170 = 30 mL is the amount of the 60% acid solution
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Check:
A: 10% of 170 = 0.10*170 = 17 mL of pure acid
B: 60% of 30 = 0.60*30 = 18 mL of pure acid
A+B = 17+18 = 35 mL of pure acid total, which matches the 35 mentioned earlier. We have confirmed the answers.