There are 3 types of milk solutions A,B and C. The ratio of the fat and non-fat contents in A, B and C is 4:3, 9:5, 5:2 respectively. If A, B and C are mixed in the ratio 2:3:4, the ratio of the fat to non fat contents in the mixture will be?

To find the ratio of fat to non-fat contents in the mixture of solutions A, B, and C, we'll proceed step-by-step by calculating the contribution of fat and non-fat parts from each solution and then combine them according to their given mixing ratios.

### Step 1: Identify Ratios of Fat and Non-Fat Content

1. **Solution A**: Fat to non-fat ratio is \(4:3\).  
   - Fat part = 4 units  
   - Non-fat part = 3 units

2. **Solution B**: Fat to non-fat ratio is \(9:5\).  
   - Fat part = 9 units  
   - Non-fat part = 5 units

3. **Solution C**: Fat to non-fat ratio is \(5:2\).  
   - Fat part = 5 units  
   - Non-fat part = 2 units

### Step 2: Determine the Proportion of Each Solution in the Mixture

Solutions A, B, and C are mixed in the ratio \(2:3:4\). So, the amounts of A, B, and C can be represented as:

- Amount of A = 2 parts
- Amount of B = 3 parts
- Amount of C = 4 parts

### Step 3: Calculate Total Fat and Non-Fat Content from Each Solution

Now, calculate the total fat and non-fat content from each solution based on their proportions.

**For Solution A (2 parts):**

- Total Fat content from A = \(2 \times 4 = 8\) units  
- Total Non-Fat content from A = \(2 \times 3 = 6\) units

**For Solution B (3 parts):**

- Total Fat content from B = \(3 \times 9 = 27\) units  
- Total Non-Fat content from B = \(3 \times 5 = 15\) units

**For Solution C (4 parts):**

- Total Fat content from C = \(4 \times 5 = 20\) units  
- Total Non-Fat content from C = \(4 \times 2 = 8\) units

### Step 4: Calculate the Total Fat and Non-Fat Contents in the Mixture

Combine the contributions from A, B, and C:

- Total Fat content in the mixture = \(8 + 27 + 20 = 55\) units
- Total Non-Fat content in the mixture = \(6 + 15 + 8 = 29\) units

### Step 5: Find the Ratio of Fat to Non-Fat Content in the Mixture

The ratio of fat to non-fat content in the mixture is:

\[
\text{Ratio} = \frac{\text{Total Fat}}{\text{Total Non-Fat}} = \frac{55}{29}
\]

So, the ratio of fat to non-fat contents in the mixture is \(\boxed{55:29}\).

Would you like more details or have any questions?

Here are some related questions:

1. What would be the ratio if the mixing ratio was different, like \(3:2:1\)?
2. How does changing the ratio of one solution affect the overall fat content?
3. Can we determine the percentage of fat content in the final mixture?
4. What happens to the overall ratio if one solution has no fat?
5. How do we calculate the ratio if given the total weight of each solution?

**Tip:** When dealing with ratios, always keep units consistent to simplify the calculation process.

Explore how to find the ratio of fat to non-fat contents when mixing milk solutions A, B, and C in specified ratios. Understand the calculation process step-by-step with detailed examples. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation