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A mixture of 45 liters of milk and water contains 20% water. How many liters of water should be added to make it a 25% water solution? Options 5 3 2 4

Question

A mixture of 45 liters of milk and water contains 20% water. How many liters of water should be added to make it a 25% water solution?

Options

  • 5
  • 3
  • 2
  • 4
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Solution

Let's solve the problem step by step.

  1. Determine the amount of water in the initial mixture:

    • The mixture is 45 liters and contains 20% water.
    • Amount of water = 20% of 45 liters = 0.20 * 45 = 9 liters.
  2. Determine the amount of milk in the initial mixture:

    • Since the total mixture is 45 liters and it contains 9 liters of water, the amount of milk is:
    • Amount of milk = 45 liters - 9 liters = 36 liters.
  3. Let x x be the amount of water to be added:

    • After adding x x liters of water, the total amount of water will be 9+x 9 + x liters.
    • The total volume of the mixture will be 45+x 45 + x liters.
  4. Set up the equation for the new concentration of water:

    • We want the new mixture to be 25% water.
    • Therefore, 9+x45+x=0.25 \frac{9 + x}{45 + x} = 0.25 .
  5. Solve the equation: 9+x45+x=0.25 \frac{9 + x}{45 + x} = 0.25 9+x=0.25(45+x) 9 + x = 0.25(45 + x) 9+x=11.25+0.25x 9 + x = 11.25 + 0.25x 9+x0.25x=11.25 9 + x - 0.25x = 11.25 0.75x=2.25 0.75x = 2.25 x=2.250.75 x = \frac{2.25}{0.75} x=3 x = 3

So, the amount of water that should be added to make the solution 25% water is 3 liters.

Answer: 3

This problem has been solved

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