10) An alloy has copper and zinc in the ratio of 6:3 and another alloy has copper and tin in the ratio of 8:6. The equal weights of both the alloys are melted to form a new alloy. What will be the weight of tin per kg of the new alloy?

Let's solve the problem step-by-step to determine the weight of tin per kilogram of the new alloy formed by melting the two given alloys together.

### Step 1: Define the Alloys

1. **Alloy 1:** Contains copper and zinc in the ratio 6:3.
2. **Alloy 2:** Contains copper and tin in the ratio 8:6.

### Step 2: Simplify the Ratios

Simplify the given ratios:

- Alloy 1: \( \text{Copper : Zinc} = 6:3 = 2:1 \)
- Alloy 2: \( \text{Copper : Tin} = 8:6 = 4:3 \)

### Step 3: Assume Equal Weights of Both Alloys

Assume that the weight of each alloy is \( x \) kg (since they are equal).

### Step 4: Calculate the Amount of Each Component in Both Alloys

1. **For Alloy 1 (weight = \( x \) kg):**
   - Copper weight: \( \frac{2}{2+1} \times x = \frac{2x}{3} \) kg
   - Zinc weight: \( \frac{1}{2+1} \times x = \frac{x}{3} \) kg

2. **For Alloy 2 (weight = \( x \) kg):**
   - Copper weight: \( \frac{4}{4+3} \times x = \frac{4x}{7} \) kg
   - Tin weight: \( \frac{3}{4+3} \times x = \frac{3x}{7} \) kg

### Step 5: Combine the Alloys to Form the New Alloy

Combine both alloys to form the new alloy:

- Total copper: \( \frac{2x}{3} + \frac{4x}{7} \) kg
- Total zinc: \( \frac{x}{3} \) kg
- Total tin: \( \frac{3x}{7} \) kg

### Step 6: Calculate the Total Weight of the New Alloy

The total weight of the new alloy is:

\[
\text{Total weight} = x + x = 2x \text{ kg}
\]

### Step 7: Find the Proportion of Tin in the New Alloy per Kilogram

The weight of tin per kilogram of the new alloy is given by:

\[
\text{Tin per kg} = \frac{\frac{3x}{7}}{2x} = \frac{3}{14} \text{ kg}
\]

### Final Answer:

The weight of tin per kilogram of the new alloy is:

\[
\frac{3}{14} \text{ kg} \approx 0.214 \text{ kg}
\]

### Do you have any questions or need further details?

Here are some related questions for further exploration:

1. How would the result change if the ratios in the alloys were different?
2. What would be the copper content per kg of the new alloy?
3. How does the presence of zinc affect the properties of the new alloy?
4. What would happen if the weights of the two alloys were not equal?
5. How do you calculate the percentage composition of each metal in the new alloy?

**Tip:** Understanding ratios and their simplifications is key in solving mixture and alloy problems effectively.

An alloy has copper and zinc in the ratio of 6:3 and another alloy has copper and tin in the ratio of 8:6. The equal weights of both the alloys are melted to form a new alloy. What will be the weight of tin per kg of the new alloy?

Learn how to determine the weight of tin per kilogram in a new alloy formed by melting two alloys with given ratios. This step-by-step solution covers key mathematical concepts like ratios and proportions, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation