Question

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 $3 per pound to get 400 pounds of the new blend. The selling price of the new blend is to be $3.50 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?

Answer 1

Let X = amount of Earl Grey tea &

Y = amount of orange pekoe tea are mixed

X + Y = 400 pounds

=> Y = 400 - X

Selling cost of Earl Grey tea = $5 per pound

Selling cost of orange pekoe tea = $3 per pound

Selling cost of mixture = $ 3.50 per pound

=> 5X + 3Y = 3.5 × 400

=> 5X + 3(400 - X) = 1400

=> 5X + 1200 - 3X = 1400

=> 2X = 1400 - 1200 = 200

=> 2X = 200

=> X = 200 / 2 = 100 pound = Earl Grey tea

=> Y = 400 - 100 = 300 pound = orange pekoe tea