How many liters of the 30% acid solution did the technician use?

Question

A lab technician combines a solution that is 30% acid by volume with a solution that is 70% acid by volume. The resulting mixture has a volume of 40 liters and is 45% acid by volume.

Accepted Answer

D. 25. Let x be the liters of 30% solution and y the liters of 70% solution. Then x + y = 40 and 0.30x + 0.70y = 0.45(40) = 18. Substituting y = 40 − x gives 0.30x + 28 − 0.70x = 18, so −0.40x = −10 and x = 25 liters (with y = 15). Check: 0.30(25) + 0.70(15) = 7.5 + 10.5 = 18 liters of acid. Choice A is the volume of the 70% solution — the correct system solved but the wrong variable reported. Choice B is 0.45(40) = 18, the number of liters of pure acid in the mixture, not the volume of the 30% solution. Choice C comes from assuming the two solutions must be used in equal amounts (half of 40), which would produce a 50% mixture, not 45%.

Answer

A. 15 — You solved the system correctly but reported y, the liters of 70% solution; the question asks for the 30% solution, which is 25 liters.

Answer

B. 18 — That's 0.45(40) = 18, the total liters of pure acid in the mixture, not the volume of the 30% solution.

Answer

C. 20 — You split 40 liters evenly, but equal amounts of 30% and 70% would give a 50% mixture; since 45% is closer to 30%, more than half must be the 30% solution.

Algebra practice question

Answer: D. 25

Why the other answers are wrong

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