A merchant mixed 8lb of a cinnamon tea with 2lb of slice tea . The 10 pound mixture cost $22. A second mixture included 14 lb of the cinnamon tea and 12 lb of the spice tea. The 26 pound mixture cost $64. Find the cost per pound of the cinnamon tea and spice tea.
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WORD PROBLEMS
Val M. asked • 03/08/17
word problems
A merchant mixed 12 lb of a cinnamon tea with 4 lb of spice tea. The 16-pound mixture cost $26. A second mixture included 16 lb of the cinnamon tea and 6 lb of the spice tea. The 22-pound mixture cost $36. Find the cost per pound of the cinnamon tea and of the spice tea.
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Danny T. answered • 03/09/17
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Let C = Cinnamon, S = Spice
Given:
12C + 4S = 26
16C + 6S = 36
Multiply 1st equation by 3, and multiply 2nd equation by 2....you will have 12S for both equations:
36C + 12S = 78 --> 12S = 78 - 36C
32C + 12S = 72 --> 12S = 72 - 32C
Set the two equations equal to each other
78 - 36C = 72 - 32C
Minus 72 on both side, and add 36C on both side
6 = 4C
C = 6/4 or 3/2 or $1.50
Plug C back into one of the original equation to solve for S
12C + 4S = 26
12(1.5) + 4S = 26
18 + 4S = 26
4S = 8
S = 2 or $2.00