Calculating Milk Percentage in a Mixture After Adding Pure Milk
Mixtures and percentage calculations are common in various fields, including chemistry, food science, and even everyday scenarios. Understanding how to manipulate these mixtures, especially when adding or removing substances, is essential for solving real-world problems. In this article, we will explore how to calculate the percentage of milk in a mixture when 5 liters of pure milk is added to 20 liters of a mixture containing 60% milk.
Initial Setup
We start with a vessel containing 20 liters of a mixture that is 60% milk. This means that the amount of milk in the mixture is calculated as follows:
Step 1: Calculate the Initial Amount of Milk
The initial amount of milk in the mixture is:
Amount of milk 0.6 times; 20 liters 12 liters
Calculation Breakdown
In a 20-liter mixture where 60% is milk, the amount of milk can be found by multiplying the total volume by the percentage of milk in decimal form:
12 liters 20 liters times; (60/100) 20 times; 0.6 12
Step 2: Calculate the Initial Amount of Water
The amount of water in the mixture is the total volume minus the amount of milk:
Amount of water 20 liters - 12 liters 8 liters
This follows the principle that the total volume of the mixture is the sum of the volumes of its components.
Adding Pure Milk
Next, we add 5 liters of pure milk to the existing mixture. This addition changes both the amount of milk and the total volume of the mixture.
Step 3: Calculate the New Amount of Milk
The new amount of milk in the mixture is the initial amount of milk plus the added milk:
New amount of milk 12 liters 5 liters 17 liters
Step 4: Calculate the New Total Volume of the Mixture
The total volume of the mixture after adding pure milk is the initial volume plus the volume of milk added:
Total volume of the mixture 20 liters 5 liters 25 liters
Calculating the New Percentage of Milk
The final step is to determine the new percentage of milk in the solution. This is done by dividing the amount of milk by the total volume of the mixture and then multiplying by 100:
Step 5: Calculate the New Percentage of Milk
Percentage of milk (17 liters / 25 liters) times; 100 68%
This calculation shows that after adding 5 liters of pure milk, the new percentage of milk in the mixture is 68%.
Conclusion
Understanding how to manipulate mixtures, such as adding pure components to a solution, is essential in various scientific and practical applications. By following these steps, we can accurately determine the new concentration of a component in a mixture after adding or removing substances.
Related Questions
Is this a problem of REMOVAL or REPLACEMENT or ADDITION?
In this case, the problem involves the ADDITION of pure milk to an existing mixture. The steps involve calculating the initial amount of milk, water, and then determining the new percentage of milk after the addition.
Conversion of Milk in Liters
The calculation is based on converting the percentage of milk in the initial mixture to liters. For the given mixture, 60% of 20 liters equals 12 liters of milk. Adding 5 liters of pure milk results in a new solution where the percentage of milk is calculated as 68%.
Additional Tips
When dealing with such problems, it's useful to first identify the type of manipulation (addition, removal, replacement) and then follow the step-by-step process to ensure accuracy. Understanding these principles helps in solving complex mixture problems efficiently.