Ask a New Question
Menu

he 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 $4 per pound with some Orange Pekoe tea that sells for $ 2 per pound to get 600 pounds of the 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 the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required

1 answer

To solve this problem, we need to set up equations based on the information provided.

Let's denote:

  • \( x \) = the amount of Earl Grey tea (in pounds)
  • \( y \) = the amount of Orange Pekoe tea (in pounds)

We know the following:

  1. The total weight of the new blend is 600 pounds.
  2. The selling price of the new blend is $2.50 per pound.

We can set up the equations:

  1. The total weight equation: \[ x + y = 600 \]

  2. The revenue from the new blend should equal the revenue if all the tea were sold separately. The revenue from the new blend is: \[ 600 \times 2.50 = 1500 \] The revenue from Earl Grey tea is: \[ 4x \] The revenue from Orange Pekoe tea is: \[ 2y \] Therefore, we set up the revenue equation: \[ 4x + 2y = 1500 \]

Now we have a system of linear equations:

  1. \( x + y = 600 \)
  2. \( 4x + 2y = 1500 \)

Next, we can solve this system. First, we can simplify the second equation by dividing everything by 2: \[ 2x + y = 750 \] Now we have a simplified system:

  1. \( x + y = 600 \) (Equation 1)
  2. \( 2x + y = 750 \) (Equation 2)

Now, we can solve for \( y \) in terms of \( x \) from Equation 1: \[ y = 600 - x \]

Substituting this expression for \( y \) into Equation 2: \[ 2x + (600 - x) = 750 \] Now simplify: \[ 2x + 600 - x = 750 \] \[ x + 600 = 750 \] Subtracting 600 from both sides: \[ x = 150 \]

Now substituting \( x = 150 \) back into the expression for \( y \): \[ y = 600 - 150 = 450 \]

Thus, the amounts required for the blend are:

  • Earl Grey tea: \( \boxed{150} \) pounds
  • Orange Pekoe tea: \( \boxed{450} \) pounds

We can also confirm that the revenue aligns with expectations:

  • Revenue from Earl Grey: \( 150 \times 4 = 600 \) dollars
  • Revenue from Orange Pekoe: \( 450 \times 2 = 900 \) dollars
  • Total Revenue: \( 600 + 900 = 1500 \) dollars

This confirms our solution is correct.