SOLUTION: A merchant mixed 10 pounds of cinnamon tea with 5 pounds of spice tea for $40.00. A second mixture included 12 pounds of cinnamon tea and 8 pounds of spice tea for $54.00. Find t

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Question 224171: A merchant mixed 10 pounds of cinnamon tea with 5 pounds of spice tea for $40.00. A second mixture included 12 pounds of cinnamon tea and 8 pounds of spice tea for $54.00. Find the cost per pound of the cinnamon tea and the spice tea.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A merchant mixed 10 pounds of cinnamon tea with 5 pounds of spice tea for $40.00. A second mixture included 12 pounds of cinnamon tea and 8 pounds of spice tea for $54.00. Find the cost per pound of the cinnamon tea and the spice tea.
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Equations:
Value Equation: 10c + 5s = 4000 cents
Value Equation: 12c + 8s = 5400 cents
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Multiply 1st by 8 and the 2nd by 5:
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80c + 40s = 8*4000
60c + 40s = 5*5400
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Subtract 2nd from 1st and solve for "c":
20c = 5000
c = 250 lbs (amount of cinnamon tea in the mix)
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Substitute into 10c+5s = 4000 to solve for "s":
10*250 + 5s = 4000
5s = 1500
s = 300 lbs (amount of spice tea in the mix)
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Cheers,
Stan H.