SOLUTION: A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18-pound mixture cost $39. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 2
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-> SOLUTION: A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18-pound mixture cost $39. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 2
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Question 332549: A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18-pound mixture cost $39. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $48. Find the cost per pound of the cinnamon tea and of the spice tea. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18-pound mixture cost $39. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $48. Find the cost per pound of the cinnamon tea and of the spice tea.
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Let x = cost per lb of cinnamon tea
and y = cost per lb of spice tea
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From:"A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18-pound mixture cost $39." we get equation 1:
12x + 6y = 39
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From:"A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $48." we get equation 2:
14x + 8y = 48
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Our system of equation is then:
12x + 6y = 39
14x + 8y = 48
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Multiplying top equation by 8 we get:
96x + 48y = 312
14x + 8y = 48
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Mutiplying bottom equation by -6 we get:
96x + 48y = 312
-84x - 48y = -288
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ADD the two equations together:
96x + 48y = 312
-84x - 48y = -288
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12x = 24
x = $2 per pound (cinnamon tea)
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Substitute the above into either of the two original equations to find y:
12x + 6y = 39
12(2) + 6y = 39
24 + 6y = 39
6y = 15
y = 15/6
y = $2.50 per pound (spice tea)
