The key idea
Track the amount of the pure substance, not the percent. Amount = concentration × volume. Mixing adds amounts and volumes; adding water adds volume only; evaporation removes water only; draining removes both in proportion.
The trap
Averaging two concentrations without weighting by volume.
Can Desmos do it?
After you write “acid before plus acid added equals acid after,” any solver finishes it. Writing that equation is the skill.
College Board skill: Percentages · Problem-Solving and Data Analysis
One question from each level. The drill has 12 at every level, and moves you up after four right in a row.
Level 1 · Warm-up
A chemist mixes 60 liters of a 5% salt solution with 40 liters of a 70% salt solution. What is the concentration of salt in the mixture, as a percent?
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Answer: 31Salt: 0.05(60)+0.7(40)=31 liters, in 100 liters of mixture. The concentration is 10031=0.31, or 31%. Simply averaging 5% and 70% ignores the different volumes.
Level 2 · Test level
How many liters of a 55% acid solution must be added to 30 liters of a 5% acid solution to make a 25% acid solution?
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Answer: 20Acid before plus acid added equals acid after: 0.05(30)+0.55x=0.25(30+x). Then 0.3x=6, so x=20 liters.
Level 3 · Beyond the test
A 40-liter salt solution is 35% salt. How many liters of water must evaporate for the solution to become 65% salt?
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Answer: 18.46Evaporation removes only water, so the salt stays at 0.35(40)=14 liters. At 65%, the total volume is 0.6514=13280 liters, so 40−13280=13240 liters evaporate.
Practice all 36 questions
Answer in the drill to get instant feedback, climb the levels, and feed your misses into Tailored practice. Free, no account.
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