Problem-Solving and Data Analysis practice question

Answer: B. 4.8

Each replacement keeps the fraction (24 − x)/24 of whatever acid is present, since the drained portion has the same concentration as the whole tank and the tank is refilled to 24 liters. After two replacements the concentration is 0.35[(24 − x)/24]² = 0.224, so [(24 − x)/24]² = 0.64 and (24 − x)/24 = 0.8. Then 24 − x = 19.2, so x = 4.8. (C) 8.64 comes from treating the situation as a single replacement: 0.35(24 − x) = 0.224(24) gives x = 8.64. (A) 4.32 is that single-replacement value split in half, as if the two identical steps simply divided one total drain evenly. (D) 9.6 is 2x, the total volume drained over both steps, which is not what the question asks for.

Why the other answers are wrong

A. 4.32

This is 8.64 ÷ 2, treating the two replacements as splitting one total drain evenly. Each step multiplies the acid by the factor (24 − x)/24, so the correct setup is 0.35[(24 − x)/24]² = 0.224.

C. 8.64

You solved as if there were only one replacement: 0.35(24 − x) = 0.224(24). The procedure happens twice, so the retention factor must be squared.

D. 9.6

That's 2x, the total volume drained across both steps. The question asks for x, the amount drained in a single replacement.

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