Understanding Proportional Mixture Calculations in Milk and Water Solutions

In the given problem, we have a 48-liter mixture of milk and water in a proportion of 5:3. This article explains how to solve such mixture problems and provides the correct solution along with the reasoning behind the calculation.

Initial Mixture Composition

Given the initial proportion of milk to water in a 48-liter mixture, we can analyze the composition.

First, let's determine the quantities of milk and water in the initial mixture:

Milk  48 / (5 3) * 5  30 litersWater  48 / (5 3) * 3  18 liters

Desired Proportion and Calculation

The goal is to add water to the mixture so that the new ratio of milk to water becomes 3:5. To solve this, let's denote the amount of water to be added as (x) liters. The new quantities will be:

According to the new proportion, we have:

Milk / Water  3 / 530 / (18   x)  3 / 5

Solving the equation for (x), we get:

30 / (18   x)  3 / 55 * 30  3 * (18   x)150  54   3x150 - 54  3x96  3xx  96 / 3x  32 liters

Hence, to achieve the desired proportion of 3:5, we need to add 32 liters of water to the initial mixture.

Conclusion and Important Points

This detailed calculation demonstrates the correct approach to solving mixture problems. It is crucial to ensure the ratios are accurately represented and the correct quantities are computed. Adding water in this manner maintains the overall volume while adjusting the composition as required.

It's worth noting that one cannot simply add water without altering the total volume or changing the proportion without adding or removing either milk or water. The key is to maintain the desired final ratio by carefully calculating the added water amount.

If you face similar mixture problems or need further assistance with chemical, biological, or pharmaceutical mixtures, this method can be applied with appropriate modifications.