Multiple choice

Sarah is conducting an experiment in her laboratory with a 15-litre solution that currently contains 45% water. To meet experimental requirements, she needs a solution with 70% water concentration. How many litres of water must Sarah carefully add to achieve this exact concentration?

  1. 6.25 litres

  2. 7.5 litres

  3. 12.5 litres

  4. 14 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial water = 0.45 * 15 = 6.75 litres. Let x be the water added. New total volume = 15 + x. New water = 6.75 + x. We need (6.75 + x) / (15 + x) = 0.70. Solving gives 6.75 + x = 10.5 + 0.7x, so 0.3x = 3.75, x = 12.5.

AI explanation

The initial 15-litre solution contains 45% water, meaning it has 6.75 litres of water and 8.25 litres of other liquid, with the other liquid remaining constant. To achieve a 70% water concentration, the 8.25 litres of non-water must represent 30% of the new total volume. We calculate the new total volume by dividing 8.25 by 0.30, which equals 27.5 litres. The amount of water Sarah must add is the difference between the new total volume and the initial volume, so 27.5 minus 15 equals 12.5 litres.

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