Ask a New Question
Menu

The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $ 5 per pound with some Orange Pekoe tea that sells for $ 2 per pound to get 900 pounds of the new blend. The selling price of the new blend is to be $ 4 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required

1 answer

To solve this problem, we can set up a system of equations based on the information given.

Let:

  • \( x \) be the number of pounds of Earl Grey tea,
  • \( y \) be the number of pounds of Orange Pekoe tea.

From the problem, we know the following:

  1. The total weight of the new blend is 900 pounds. This gives us our first equation: \[ x + y = 900 \]

  2. The cost of the blend must equal the revenue from selling the blend. The revenue from selling 900 pounds at $4 per pound is: \[ 900 \times 4 = 3600 \text{ dollars} \] Now we express the cost of the teas:

    • The cost of \( x \) pounds of Earl Grey tea at $5 per pound is \( 5x \).
    • The cost of \( y \) pounds of Orange Pekoe tea at $2 per pound is \( 2y \).

    Therefore, the total cost of the blend can be expressed as: \[ 5x + 2y \]

    Setting the cost equal to the revenue, we have the second equation: \[ 5x + 2y = 3600 \]

Now we have a system of equations:

  1. \( x + y = 900 \)
  2. \( 5x + 2y = 3600 \)

We can solve this system step by step.

From the first equation, we can express \( y \) in terms of \( x \): \[ y = 900 - x \]

Now substitute \( y \) in the second equation: \[ 5x + 2(900 - x) = 3600 \]

Distributing the \( 2 \): \[ 5x + 1800 - 2x = 3600 \]

Combining like terms: \[ 3x + 1800 = 3600 \]

Subtracting 1800 from both sides: \[ 3x = 1800 \]

Dividing by 3: \[ x = 600 \]

Substituting \( x \) back into the first equation to find \( y \): \[ y = 900 - 600 = 300 \]

Thus, the store needs:

  • 600 pounds of Earl Grey tea
  • 300 pounds of Orange Pekoe tea

Final Answer: 600 pounds of Earl Grey tea and 300 pounds of Orange Pekoe tea.