SOLUTION: A merchant mixed 12 lb of a cinnamon tea with 4 lb of spice tea. The 16-pound mixture cost $42. A second mixture included 16 lb of the cinnamon tea and 8 lb of the spice tea. The 2
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Question 501601: A merchant mixed 12 lb of a cinnamon tea with 4 lb of spice tea. The 16-pound mixture cost $42. A second mixture included 16 lb of the cinnamon tea and 8 lb of the spice tea. The 24-pound mixture cost $64. Find the cost per pound of the cinnamon tea and of the spice tea.
12 x + 4 y = 42 .............1
16 x + 8 y = 64 .............2
Eliminate y
multiply (1)by -2
Multiply (2) by 1
-24 x -8 y = -84
16 x 8 y = 64
Add the two equations
-8 x = -20
/ -8
x = 2.50
plug value of x in (1)
12 x + 4 y = 42
30 + 4 y = 42
4 y = 42 -30
4 y = 12
y = 3.00
cinnamon tea 2 1/2 $/kg
spice tea 3 $/kg
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