A solution of vinegar and water contains 2 litres of vinegar and 6 litres of water. How much pure vinegar
must be added to this solution so that the resulting solution will be 2/3 vinegar.


To solve this problem, let's define the variables and break it down step by step.

### Variables:
- The initial amount of vinegar in the solution: 2 litres.
- The initial amount of water in the solution: 6 litres.
- Let \( x \) be the amount of pure vinegar to be added to the solution.

### Step-by-Step Solution:
1. **Initial total volume of the solution:**
   The total volume of the solution initially is:
   \[
   \text{Initial total volume} = 2 \text{ litres of vinegar} + 6 \text{ litres of water} = 8 \text{ litres}.
   \]

2. **Total volume after adding pure vinegar:**
   After adding \( x \) litres of pure vinegar, the total volume of the new solution becomes:
   \[
   \text{New total volume} = 8 + x.
   \]

3. **Vinegar content in the new solution:**
   The new amount of vinegar in the solution is:
   \[
   \text{New vinegar content} = 2 + x.
   \]

4. **Condition for the final concentration:**
   We are told that the resulting solution should be \( \frac{2}{3} \) vinegar. This means:
   \[
   \frac{\text{Vinegar content}}{\text{Total volume}} = \frac{2}{3}.
   \]
   Substituting the values:
   \[
   \frac{2 + x}{8 + x} = \frac{2}{3}.
   \]

5. **Solve the equation:**
   Now, we solve for \( x \):
   \[
   3(2 + x) = 2(8 + x).
   \]
   Expanding both sides:
   \[
   6 + 3x = 16 + 2x.
   \]
   Simplifying:
   \[
   3x - 2x = 16 - 6,
   \]
   \[
   x = 10.
   \]

### Conclusion:
You need to add **10 litres of pure vinegar** to the solution for the resulting solution to be \( \frac{2}{3} \) vinegar.

---

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you find the concentration of a solution if both components are given?
2. What if we had 4 litres of vinegar and 8 litres of water? How would that change the answer?
3. How do you solve for an unknown in a proportion equation?
4. What are other methods to calculate the concentration of a solution?
5. How would you approach this problem if you were adding water instead of vinegar?

**Tip:** Always double-check units and ensure that total amounts align with the conditions given in the problem.

A solution of vinegar and water contains 2 litres of vinegar and 6 litres of water. How much pure vinegar must be added to this solution so that the resulting solution will be 2/3 vinegar?

Learn how to solve a mixture problem involving vinegar and water, where the solution initially contains 2 litres of vinegar and 6 litres of water. Find out how much pure vinegar must be added to make the solution 2/3 vinegar. Suitable for Grades 8-10.

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