SOLUTION: A merchant mixed 12 lb of a cinnamon tea with 5 lb of spice tea. The 17-pound mixture cost $28. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 2

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Question 1169996: A merchant mixed 12 lb of a cinnamon tea with 5 lb of spice tea. The 17-pound mixture cost $28. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $37. Find the cost per pound of the cinnamon tea and of the spice tea.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
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Not much different from this one except a few of the given values:
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1169909.html
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1169909.html

Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
A merchant mixed 12 lb of a cinnamon tea with 5 lb of spice tea. The 17-pound mixture cost $28.
A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $37.
Find the cost per pound of the cinnamon tea and of the spice tea.
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    12x + 5y = 28   dollars     (1)

    14x + 8y = 37   dollars     (2)


Multiply equation (1) by 8 (both sides).

Multiply equation (2) by 5 (both sides).  You will get


    96x + 40y = 28*8            (3)

    70x + 40y = 37*5            (4)


From equation (3), subtract equation (4).  You will get


    26x       = 28*8 - 37*5 = 39

      x                     = 39/26 = 3%2F2 = 1.50  dollars.


To find y, substitute the found value x= 1.50 into equation (1). You will get


    12*1.50 + 5y = 28

    18      + 5y = 28

              5y = 28-18 = 10

               y         = 10/2 = 5.


ANSWER.  Cinamon tea price is $1.50 per pound.  The spice tea price is $2.00 dollars per pound.

Solved.

The method I used in the solution, is called the ELIMINATION method.