If 5 liters of a mixture of milk and water contains 60% milk, how much water mus

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Question: If 5 liters of a mixture of milk and water contains 60% milk, how much water must be added to make the mixture 40% milk?

Options:

Correct Answer: 4 liters

Solution:

Initial milk = 60% of 5L = 3L. Let x be the liters of water added. New total = 5 + x. We need 3/(5+x) = 0.4. Solving gives x = 4L.

If 5 liters of a mixture of milk and water contains 60% milk, how much water must be added to make the mixture 40% milk?

If 5 liters of a mixture of milk and water contains 60% milk, how much water must be added to make the mixture 40% milk?

Step 1: Calculate the amount of milk in the initial mixture. Since the mixture is 60% milk and the total volume is 5 liters, multiply 5 liters by 60% (or 0.6). This gives you 3 liters of milk.
Step 2: Let x be the amount of water you need to add. The new total volume of the mixture will be 5 liters (initial mixture) plus x liters (water added), which is 5 + x liters.
Step 3: Set up the equation to find the new percentage of milk in the mixture. We want the milk to be 40% of the new total volume. This means we need to set up the equation: 3 liters (milk) divided by (5 + x) liters (new total) equals 0.4.
Step 4: Write the equation: 3 / (5 + x) = 0.4.
Step 5: Solve the equation for x. First, multiply both sides by (5 + x) to eliminate the fraction: 3 = 0.4 * (5 + x).
Step 6: Distribute 0.4 on the right side: 3 = 2 + 0.4x.
Step 7: Subtract 2 from both sides to isolate the term with x: 1 = 0.4x.
Step 8: Divide both sides by 0.4 to solve for x: x = 1 / 0.4, which equals 2.5 liters.
Step 9: Therefore, you need to add 2.5 liters of water to make the mixture 40% milk.

Percentage and Proportions – Understanding how to calculate percentages and set up proportions based on the mixture's composition.
Algebraic Manipulation – Using algebra to solve for an unknown variable in an equation derived from the problem.
Mixture Problems – Applying concepts of mixtures to determine the required quantities to achieve a desired concentration.