Question
Asked Oct 14, 2019
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A merchant mixed 10 lb of a cinnamon tea with 6 lb of spice tea. The 16-pound mixture cost $27. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $37. Find the cost per pound of the cinnamon tea and of the spice tea.

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Expert Answer

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Let the cost per pound of cinnamon and spice tea be x and y Then, the cost of 10 pounds cinnamon tea and that of 6 pounds spice tea will be 10x and 6y Since the cost of two variety of tea is $27, then their the mathematical equation is 10x6y 27 Similarly, the cost of 14 pounds cinnamon tea and that of 8 pounds spice tea will be 14x and 8y Since the cost of two variety of tea is $37, then their the mathematical equation is 14x+8y 37

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Solve the equations 14x +8y 37 and 10x 6y 27 as follows - Multiply by 3 to equation 14x 8y =37 and 4 by to the equation 10x 6y 27 That is, the new equation are 42x 24y -111 and 40x +24y 108 Subtract the equation 40x +24y108 from the equation 42x 24y =111 and solve forx 42х + 24у - (40х + 24у) %3D111-108 2х —0%3 3 3 =1.5 2 X

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