SOLUTION: A merchant mixed 8 lb of a cinnamon tea with 4 lb of spice tea. The 12-pound mixture cost $38. A second mixture included 10 lb of the cinnamon tea and 12 lb of the spice tea. The 2

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A merchant mixed 8 lb of a cinnamon tea with 4 lb of spice tea. The 12-pound mixture cost $38. A second mixture included 10 lb of the cinnamon tea and 12 lb of the spice tea. The 2      Log On

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Question 584607: A merchant mixed 8 lb of a cinnamon tea with 4 lb of spice tea. The 12-pound mixture cost $38. A second mixture included 10 lb of the cinnamon tea and 12 lb of the spice tea. The 22-pound mixture cost $72. Find the cost per pound of the cinnamon tea and of 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+=+38+
and
(2) +10a+%2B+12b++=+72+
-------------------
Multiply both sides of (1) by 3
and subtract (2) from (1)
(1) +24a+%2B+12b+=+114+
(2) +-10a+-+12b+=+-72+
+14a+=+42+
+a+=+3+
and
(1) +8%2A3+%2B+4b+=+38+
(1) +24+%2B+4b+=+38+
(1) +4b+=+14+
(1) +b+=+3.5+
The cost/pound of cinnamon tea is $3
The cost/pound of spice tea is $3.50
check:
(2) +10%2A3+%2B+12%2A3.5++=+72+
(2) +30+%2B+42+=+72+
(2) +72+=+72+
OK