Correcting the Milk-to-Water Ratio: A Seo-Optimized Guide

In this guide, we will walk you through solving a classic problem in proportions and ratios. You will learn how to adjust the mixture of milk and water to achieve the desired ratio of 3:2. This solution involves understanding and applying basic algebraic principles to ensure the correct balance of components in your mixture.

Problem Statement

Suppose a milkman has a mixture of 8 liters of milk and water where the quantity of milk is equal to the quantity of water. The mixture needs to be adjusted to a 3:2 ratio of milk to water. Here is how you can solve this problem.

Current Situation

The milkman has 8 liters of a mixture which is half milk and half water:

- Milk: 4 liters (since 8/2 4) - Water: 4 liters (since 8/2 4)

Desired Ratio

We want to achieve a ratio of milk to water of 3:2.

Let:

- m be the amount of milk in liters, - w be the amount of water in liters.

From the desired ratio we can express it as:

3m 2w

Expressing Water in Terms of Milk

From the ratio we can express water as:

W (2/3) * m

Total Mixture

The total mixture is given by:

W W 8 x
where x is the amount of water to be added.

Substituting the Amount of Milk

Sinces m 4 liters, we can substitute m into the equation:

4 (2/3)*4*x 8 x

Simplifying the Equation

Substituting w:

4 (8/3)*x 8 x

Solving for x:

Subtracting 4 from both sides:

(8/3)*x 4 x

Rearranging gives:

(8/3)*x - x 4

This is incorrect as it suggests adding water, but in reality, more needs to be removed.

Finding the Correct Amount of Water

To satisfy the 3:2 ratio with the current amounts, total parts 3 parts milk 2 parts water 5 parts.

For every 3 parts of milk, we need 2 parts of water.

Let’s denote the total milk to be m 4 liters. Therefore the required amount of water w should be:

w (2/3) * 4 8/3 liters.

Current Amount of Water

Currently there are 4 liters of water in the mixture. To find out how much more water to add:

(8/3) - 4 (8/3) - (12/3) -4/3

This means that we have too much water already.

Conclusion

To achieve the desired ratio of 3:2, the milkman actually needs to remove water as he has already added too much water. Specifically, he should remove (4/3) liters of water from the mixture to achieve the correct ratio of 3 parts milk to 2 parts water.