The manager of a store that specializes in selling tea decides to experiment with a new blend she will mix some earl gray tea that sells for 5$ per pound with some orange pekoe tea that sells for 2$ per pound to get 900 pounds of a new blend the selling price of the new blend is to be 2.50$ per pound and there is to be no difference in revenue from selling the new blend versus selling other types how many pounds of the earl grey tea and orange pekoe tea are required 

We need to determine how many pounds of Earl Grey tea and Orange Pekoe tea should be mixed to create 900 pounds of a new blend that will sell for $2.50 per pound, while keeping the revenue the same as if each type of tea was sold separately.

Let:
- $ x $ = pounds of Earl Grey tea (which costs $5 per pound),
- $ y $ = pounds of Orange Pekoe tea (which costs $2 per pound).

We have two pieces of information:
1. The total weight of the blend is 900 pounds:
   \[
   x + y = 900
   \]
2. The total cost of the blend must equal the total revenue as if the individual teas were sold separately. So, the total cost of the new blend is $ 900 \times 2.50 = 2,250 $ dollars. Therefore, the total cost equation is:
   \[
   5x + 2y = 2,250
   \]

Now, we have the system of equations:
\[
1. \quad x + y = 900
\]
\[
2. \quad 5x + 2y = 2,250
\]

### Step 1: Solve for one variable
From the first equation, solve for $ y $ in terms of $ x $:
\[
y = 900 - x
\]

### Step 2: Substitute this into the second equation
Substitute $ y = 900 - x $ into the second equation:
\[
5x + 2(900 - x) = 2,250
\]

### Step 3: Simplify and solve for $ x $
\[
5x + 2(900 - x) = 2,250
\]
\[
5x + 1,800 - 2x = 2,250
\]
\[
3x + 1,800 = 2,250
\]
\[
3x = 2,250 - 1,800
\]
\[
3x = 450
\]
\[
x = \frac{450}{3} = 150
\]

### Step 4: Solve for $ y $
Substitute $ x = 150 $ into the first equation:
\[
150 + y = 900
\]
\[
y = 900 - 150 = 750
\]

### Final Answer:
The manager should mix:
- 150 pounds of Earl Grey tea,
- 750 pounds of Orange Pekoe tea.

This will produce the desired 900-pound blend that sells for $2.50 per pound, maintaining the same revenue.

---

Do you have any questions, or would you like further details?  
Here are 5 related questions for practice:
1. What would the proportions be if the price of the new blend was set at $3 per pound?
2. How would the mix change if the total weight was 1,000 pounds instead of 900 pounds?
3. What if Earl Grey tea cost $6 per pound instead of $5?
4. If the price of Orange Pekoe tea increased to $3 per pound, how would the blend proportions be affected?
5. What would be the revenue if only 500 pounds of the new blend were sold at $2.50 per pound?

**Tip:** When working with cost and mixture problems, always set up equations based on both total quantity and total value to ensure consistency in results.

The manager of a store that specializes in selling tea decides to experiment with a new blend she will mix some earl gray tea that sells for 5$ per pound with some orange pekoe tea that sells for 2$ per pound to get 900 pounds of a new blend the selling price of the new blend is to be 2.50$ per pound and there is to be no difference in revenue from selling the new blend versus selling other types how many pounds of the earl grey tea and orange pekoe tea are required

Learn how to solve a system of equations to determine how many pounds of Earl Grey and Orange Pekoe tea are needed to create a 900-pound blend. This problem involves linear equations and substitution, making it ideal for students in Grades 8-10.

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