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To solve the problem:

The tea shop owner is blending **two teas**:
- Tea A costs **$5.40 per pound**.
- Tea B costs **$6.80 per pound**.
- The owner wants **8 pounds** of the blend priced at **$5.75 per pound**.

Let:
- $ x $ = pounds of Tea A
- $ y $ = pounds of Tea B

We need two equations:
1. The total weight of the blend:
   \[
   x + y = 8
   \]
2. The total cost of the blend:
   \[
   5.40x + 6.80y = 5.75(8)
   \]

---

### Solving the system:
1. From the first equation $ x + y = 8 $, solve for $ y $:
   \[
   y = 8 - x
   \]

2. Substitute $ y = 8 - x $ into the second equation:
   \[
   5.40x + 6.80(8 - x) = 5.75(8)
   \]

3. Simplify:
   \[
   5.40x + 6.80(8) - 6.80x = 5.75(8)
   \]
   \[
   5.40x + 54.4 - 6.80x = 46
   \]

4. Combine like terms:
   \[
   (5.40 - 6.80)x + 54.4 = 46
   \]
   \[
   -1.40x + 54.4 = 46
   \]

5. Solve for $ x $:
   \[
   -1.40x = 46 - 54.4
   \]
   \[
   -1.40x = -8.4
   \]
   \[
   x = \frac{-8.4}{-1.40}
   \]
   \[
   x = 6
   \]

6. Now find $ y $:
   \[
   y = 8 - x
   \]
   \[
   y = 8 - 6
   \]
   \[
   y = 2
   \]

---

### Final Answer:
- The owner should use **6 pounds of Tea A** and **2 pounds of Tea B**.

---

### Verification:
- Total weight: $ 6 + 2 = 8 $ ✔
- Total cost:
   \[
   5.40(6) + 6.80(2) = 32.4 + 13.6 = 46
   \]
   - Average price: $ \frac{46}{8} = 5.75 $ ✔

---

### Do you need further clarification?  
Here are 5 related questions:
1. How do you solve a similar mixture problem with 3 ingredients?
2. What if the total weight or price per pound changes?
3. How can this method be applied to percentages instead of costs?
4. What are the graphical solutions of these systems of equations?
5. How do you verify your solution for a weighted average?

**Tip:** Always check both constraints (weight and cost) when solving systems of equations for mixtures.

The owner of a tea shop is making a blend of two teas. Tea A costs $5.40 per pound. Tea B costs $6.80 per pound. The owner wants to make 8 pounds of the blend and wants to sell it for $5.75 per pound. How much of each tea should he use?

Learn how to solve a tea mixture problem where two teas with different costs are blended to achieve a target price. This problem involves systems of equations and weighted averages, ideal for Grades 8-10 algebra students.

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