SOLUTION: A merchant mixed 8 lb of a cinnamon tea with 4 lb pf spice tea. The 12 pound mixture cost $14. A second mixture included 12 lb of the cinnamon tea and 12 lb of the spice tea. The 2

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: A merchant mixed 8 lb of a cinnamon tea with 4 lb pf spice tea. The 12 pound mixture cost $14. A second mixture included 12 lb of the cinnamon tea and 12 lb of the spice tea. The 2      Log On

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Question 1050539: A merchant mixed 8 lb of a cinnamon tea with 4 lb pf spice tea. The 12 pound mixture cost $14. A second mixture included 12 lb of the cinnamon tea and 12 lb of the spice tea. The 24 pound mixture cost $30. Find the coat per pound of the cinnamon tea and the spice tea.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = cost/pound of cinnamon tea
Let +b+ = cost/pound of spice tea
---------------------------------------
(1) +8a+%2B+4b+=+14+
(2) +12a+%2B+12b+=+30+
--------------------------
(1) +4a+%2B+2b+=+7+
(2) +2a+%2B+2b+=+5+
--------------------------
Subtract (2) from (1)
+2a+=+2+
+a+=+1+
and
(2) +2%2A1+%2B+2b+=+5+
(2) +2+%2B+2b+=+5+
(2) +2b+=+3+
(2) +b+=+1.5+
-------------------
$1.50 = cost/pound of spice tea
$1.00 = cost/pound of cinnamon tea
-----------------------------------
check:
(1) +4a+%2B+2b+=+7+
(1) +4%2A1+%2B+2%2A1.5+=+7+
(1) +4+%2B+3+=+7+
and
(2) +2a+%2B+2b+=+5+
(2) +2%2A1+%2B+2%2A1.5+=+5+
(2) +2+%2B+3+=+5+
OK