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The problem in the image states the following:

- In Jar A, there are 10 liters of milk and 6 liters of water.
- In Jar B, there is 65 liters of a milk and water solution, where the ratio of milk to water is \(10 : x\).
- Jars A and B are emptied into Jar C, which has a total of 9 liters of water.
- Jar C now has 75% milk.
  
We are tasked with finding the value of \(x\) (the ratio in Jar B).

---

Let's break this down:

1. **Jar A**: 
   - Milk: 10 liters
   - Water: 6 liters

2. **Jar B**:
   - Total solution: 65 liters
   - Ratio of milk to water is \(10 : x\)
   - So, the amount of milk in Jar B is \( \frac{10}{10+x} \times 65 \) liters.
   - The amount of water in Jar B is \( \frac{x}{10+x} \times 65 \) liters.

3. **Jar C** (after combining Jars A and B):
   - Water: 9 liters already + water from Jar A + water from Jar B
   - Milk will be 75% of the total volume of Jar C.

---

### Step 1: Total Milk in Jar C
From Jar A: 10 liters of milk  
From Jar B: Milk from Jar B is \( \frac{10}{10+x} \times 65 \).

Total milk in Jar C = \( 10 + \frac{10}{10+x} \times 65 \).

### Step 2: Total Water in Jar C
Water from Jar A: 6 liters  
Water from Jar B: \( \frac{x}{10+x} \times 65 \) liters  
Water already in Jar C: 9 liters

Total water in Jar C = \( 6 + \frac{x}{10+x} \times 65 + 9 \).

### Step 3: Total Volume in Jar C
The total volume in Jar C (milk + water) is:
\[
\text{Total volume} = \text{Total milk} + \text{Total water}.
\]
This simplifies to:
\[
10 + \frac{10}{10+x} \times 65 + 6 + \frac{x}{10+x} \times 65 + 9.
\]

### Step 4: Applying the Milk Percentage
It is given that Jar C has 75% milk, so the fraction of milk is:
\[
\frac{\text{Total milk}}{\text{Total volume}} = 0.75.
\]

Substituting the expressions for total milk and total volume into this equation gives a solvable equation in terms of \(x\). Solving this will yield the value of \(x\). 

---

Let me calculate the exact value for you.

### Step 5: Solving the Equation
The milk-to-total ratio is \(0.75\), and setting up the equation will give:

\[
\frac{10 + \frac{10}{10+x} \times 65}{10 + \frac{10}{10+x} \times 65 + 6 + \frac{x}{10+x} \times 65 + 9} = 0.75.
\]

Multiplying through and solving this equation will give the value of \(x\).

---

I'll calculate this for you now:

\[
\frac{10 + \frac{650}{10+x}}{25 + 65} = 0.75
\]

This simplifies into finding \(x\).



In Jar A, there are 10 liters of milk and 6 liters of water. In Jar B, there is 65 liters of a milk and water solution having a milk to water ratio as 10 : x. Jars A and B are emptied into Jar C which has 9 liters of water. If Jar C has 75% milk, then the value of x is:

Solve this milk-water mixture problem involving ratios and percentages. Learn how to calculate the correct ratio (x) by applying key mixture concepts and algebraic equations. Perfect for students in Grades 9-12.

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