Multiple choice

Lisa is making a mixture by combining two vinegar solutions. The first solution has 3 liters with a 25% concentration, and the second solution has 6 liters with a stronger concentration. After mixing, she gets 9 liters of a solution with a 40% concentration. What percentage concentration did the second solution originally have?

  1. 35.7%

  2. 45.5%

  3. 47.5%

  4. 55.8%

  5. 75.5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total volume = 9L. Total vinegar = 40% of 9 = 3.6L. First solution: 25% of 3L = 0.75L. Second solution: 3.6 - 0.75 = 2.85L. Concentration = 2.85 / 6 = 0.475 = 47.5%.

AI explanation

Using the method of alligation, the ratio of the volume of the first solution to the second solution is 3 to 6, which simplifies to 1 to 2. Setting up the alligation calculation gives 1 part multiplied by (47.5 minus 40) equals 2 parts multiplied by (40 minus 25). This confirms the second solution originally had a 47.5% concentration.

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