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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 $6 per pound with some Orange Pekoe tea that sells for $4 per pound to get 600 pounds of the new blend. the selling price of the new blend is $4.50 per pound and there was something 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?

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Respuesta :

sqdancefan

Answer:

  • Earl Grey: 150 pounds
  • Orange Pekoe: 450 pounds

Step-by-step explanation:

Let "e" represent the number of pounds of Earl Grey tea required for the mix. Then (600-e) is the number of pounds of Orange Pekoe tea required. The total cost of the mix is ...

  6·e + 4·(600 -e) = 4.50·600

  2e = 600·(4.50 -4.00) . . . . . simplify, subtract 4·600

  e = 300/2 = 150 . . . . . . . . . . divide by the coefficient of x

Required are 150 pounds of Earl Grey and 450 pounds of Orange Pekoe.

fichoh

The amount of Earl Grey and Pekoe tea required for the new blend is :

  • 150 pounds of Earl
  • 450 pounds of Pekoe

Price of new blend per pound = $4.50

Price per pound of Earl tea = $6

Price per pound of Pekoe tea = $4

Let :

Pound of Earl tea = a

Pound of Pekoe tea = b

Converting the information to Mathematical expressions :

  • a + b = 600 - - - (1)
  • 6a + 4b = 600(4.50)
  • 6a + 4b = 2700 - - - (2)

From (1):

a = 600 - b

Put a = 600 in (2)

6(600 - b) + 4b = 2700

3600 - 6b + 4b = 2700

Collect like terms :

-6b + 4b = 2700 - 3600

-2b = -900

b = 900 ÷ 2

b = 450

Recall :

a = 600 - b

a = 600 - 450

a = 150

Therefore,

  • Pound of Earl tea required = 150
  • Pound of Pekoe tea required = 450

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