SOLUTION: A merchant mixed 8 lb of a cinnamon tea with 2 lb of spice tea. The 10-pound mixture cost $16. A second mixture included 12 lb of the cinnamon tea and 14 lb of the spice tea. The 2

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Question 1017066: A merchant mixed 8 lb of a cinnamon tea with 2 lb of spice tea. The 10-pound mixture cost $16. A second mixture included 12 lb of the cinnamon tea and 14 lb of the spice tea. The 26-pound mixture cost $46. Find the cost per pound of the cinnamon tea and of the spice tea.
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let the price variables be c for the cinnamon and s for the spice teas.

The 10 pound mixture cost: 8c%2B2s=16

The 26 pound mixture cost: 12c%2B14s=46

Simplify the equations in forming the system.
system%284c%2Bs=8%2C6c%2B7s=23%29
and choose your method to finish solving.

highlight%28system%28c=1%261%2F2%2Cs=2%29%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A merchant mixed 8 lb of a cinnamon tea with 2 lb of spice tea. The 10-pound mixture cost $16. A second mixture included 12 lb of the cinnamon tea and 14 lb of the spice tea. The 26-pound mixture cost $46. Find the cost per pound of the cinnamon tea and of the spice tea.
let c=cost per pound of cinnamon tea
let s=cost per pound of spice tea
8c+2s=16
12c+14s=46
56c+14s=112
12c+14s=46
subtract:
44c=66
c=66/44
c=1.50
2s=16-8c
2s=4.00
s=2.00
cost per pound of cinnamon tea=$1.50
cost per pound of spice tea=$2.00