Multiple choice

There are 4 bottles of equal volume containing sugar solution. Each bottle is filled at least up to 40% of its capacity. The concentrations of the solutions in the four bottles are 20%, 30%, 50%, and 70%, respectively. If the solutions of these four bottles are emptied into a large container and mixed properly, what can be the minimum and maximum concentration of sugar in the resulting mixture?

  1. Minimum = 32.0%, Maximum = 57.5%

  2. Minimum = 35.0%, Maximum = 50.0%

  3. Minimum = 36.5%, Maximum = 60.0%

  4. Minimum = 37.5%, Maximum = 52.5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The mixture concentration depends on the volume of each solution. Since each bottle is at least 40% full, the total volume is between 1.6 and 4.0 units. The weighted average of concentrations (20, 30, 50, 70) will be minimized when the lower concentration bottles are at maximum capacity and maximized when the higher concentration bottles are at maximum capacity.

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