SOLUTION: Please help me with this question! A merchant blends tea that sells for $5.05 a pound with tea that sells for $2.80 a pound to produce 90 lb of a mixture that sells for $3.30 a

Question 659516: Please help me with this question!
A merchant blends tea that sells for $5.05 a pound with tea that sells for $2.80 a pound to produce 90 lb of a mixture that sells for $3.30 a pound. How many pounds of each type of tea does the merchant use in the blend?
Thank you!
Answer by kevwill(135) (Show Source): You can put this solution on YOUR website!
Let x be the weight of the expensive tea, and y be the weight of the cheaper tea. The merchant produces 90 pounds of tea, so
x + y = 90.
The price of the tea is:
5.05*x + 2.80*y = 3.30*90 = 297
In the first equation, subtract x from both sides to give:
y = 90 - x
Substituting for y in the second equation gives:
5.05*x + 2.80*(90-x) = 297
Expanding:
5.05*x + 252 - 2.80*x = 297
Combine terms and subtract 252 from each side:
2.25*x = 45
Divide both sides by 2.25:
x = 45/2.25 = 20
So the merchant uses 20 pounds of the expensive team and 70 pounds of the cheaper tea.

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