Math Problem Statement
there is a 25 litre mixture of milk and water, containing milk and water in the ratio 3:2, find the number of litres of water that should be added to the mixture so that the resultant mixture has 50% water in it.
Solution
We are given a 25-litre mixture of milk and water, where the ratio of milk to water is . We need to find how many litres of water should be added so that the final mixture contains 50% water.
Step-by-Step Solution:
-
Find the current amount of milk and water in the mixture:
-
Total volume of the mixture = 25 litres.
-
Ratio of milk to water = , so the fraction of milk is and the fraction of water is .
-
Amount of milk = litres.
-
Amount of water = litres.
-
-
Let the amount of water to be added be litres.
- After adding litres of water, the new amount of water becomes litres.
- The total volume of the new mixture becomes litres.
-
Set up the equation for 50% water in the new mixture:
- For the resultant mixture to have 50% water, the amount of water should be half of the total volume of the mixture.
-
Solve the equation:
Final Answer:
You need to add 5 litres of water to the mixture so that the resultant mixture has 50% water.
Would you like further clarification or additional details on any step? Here are some related questions you might find interesting:
- What if the original ratio of milk to water was different, say 4:1?
- How many litres of water should be added to make the mixture 40% water instead of 50%?
- What would happen if we added milk instead of water to the mixture? How would the ratio change?
- How can you determine the percentage of water in any mixture if given its ratio?
- Can you create an equation to represent the percentage of a liquid in a mixture based on its initial ratio?
Tip: Always check if the units and percentages in your mixture problems add up correctly to avoid errors!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Ratios
Algebra
Linear Equations
Formulas
Ratio formula
Equation for percentage in a mixture
Theorems
Percentage theorem for mixtures
Suitable Grade Level
Grades 7-9
Related Recommendation
Calculating Water Addition in Milk-Water Mixture to Achieve Desired Milk Percentage
Finding Equal Milk Percentage in Mixed Solutions: Volume Transfer Calculation
Find the Ratio in Mixture Problem with Milk and Water Using Percentages
How to Mix Liquids to Achieve a 50% Milk and 50% Water Mixture
Calculate Milk Percentage in a Water-Milk Mixture After Adding Pure Milk