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application problem please help

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A merchant mixed 8 lb of a cinnamon tea with 4 lb of spice tea. The 12-pound mixture cost $20. A second mixture included 10 lb of the cinnamon tea and 16 lb of the spice tea. The26-pound mixture cost $47. Find the cost per pound of the cinnamon tea and of the spice tea.

Oct 20th, 2017

Let cost of per pound of cinnamon tea be x and that of spice tea be y.

so we get,

8x+4y=20 and 10x+16y =47

solving two equations by elimination. mulitplying the 1st eq by 4 ans subtracting from 2nd equation.

10x+16y- (32x +16y) = 47-80
-22x = -33
x  = 33/22 = 3/2 = 0.67 dollars
and from equation on. 8*(3/2) + 4y = 20
4y = 8
y = 2 dollars

so, cinnamon tea costs 0.67 dollars per pound and
spice tea costs 2 dollars per pound

Apr 21st, 2015

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