SOLUTION: 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 t

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Question 1199489: 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 100 pounds of the new blend. The selling price of the new blend is to be $4.50 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 Early Grey tea and Orange Pekoe tea are required?


Too many words here. I seek the correct equation setup.


Thanks
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Earl Grey $5 per pound
Pekoe $3 per pound
100 pounds for $4.5 per pound

Notice that at the price desired, manager will use more of the Earl Gray than the Orange Pekoe.

v of Earl Gray
100-v of the Pekoe

5v%2B3%28100-v%29=4.5%2A100--------- a correct equation based on variable assignment


5v%2B3%2A100-3v=4.5%2A100
%285-3%29v=4.5%2A100-3%2A100
v=%284.5%2A100-3%2A100%29%2F%285-3%29
v=100%28%284.5-3%29%2F%285-3%29%29--------Observe this form of the solution, how it relates to the description, before computing it.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let x = pounds of Earl Grey tea at $5 per pound
Then 100-x = pounds of Orange Pekoe tea at $3 per pound

The revenue from the two batches of tea separately is to be the same as the revenue from the blend:

5%28x%29%2B3%28100-x%29=4.5%28100%29

You asked only for the equation setup; there it is....

Note that, since the price per pound of the blend is closer to the price per pound of the Earl Grey tea, the amount of Earl Grey tea will be greater than the amount of Orange Pekoe tea.

To take that idea a bit further, if a formal algebraic solution is not required, this problem can be solved quickly by observing that the price of the blend is 3/4 of the way from the price of the Orange Pekoe tea to the price of the Earl Grey tea ($3 to $5 is a difference of $2.00; $3 to $4.50 is a difference of $1.50; 1.50/2.00 = 3/4.)

That means 3/4 of the blend must be the Earl Grey tea.

ANSWER (which you should get by solving the equation shown above): 75 pounds of Earl Grey tea; 25 pounds of Orange Pekoe tea.