Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18-pound mixture cost $48. A second mixture included 16 lb of the...?

A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18-pound mixture cost $48. A second mixture included 16 lb of the cinnamon tea and 10 lb of the spice tea. The 26-pound mixture cost $70. Find the cost per pound of the cinnamon tea and of the spice tea.

cinnamon =       dollars per poundspice =              dollars per pound

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  • alex
    Lv 7
    6 months ago
    Favorite Answer

    12c + 6s = 48

    16c + 10s = 70

    solve 2 equations for c , s

  • Philip
    Lv 6
    6 months ago

    Put [cinnamon, spice] tea = [ct,st].

    Then 12ct +  6st = $48, ie., 2ct +   st = $8.... (1).

    and...16ct +10st = $70, ie., 8ct + 5st = $35...(2).

    [(2)-4(1)] ---> st =   $(35-32)    = $3.

    Then (1) ---> ct =   $(1/2)(8-3) = $(2.5). 

    So [cinnamon,spice] tea cost $[3 , 2.5] per pound.

  • 6 months ago

    A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. 

     The 18-pound mixture cost $48. 

     A second mixture included 16 lb of the cinnamon tea and 10 lb of the spice tea. 

     The 26-pound mixture cost $70. 

     Find the cost per pound of the cinnamon tea and of the spice tea.

    12x + 6y = 48

    16x + 10y = 70

    60x + 30y = 240

    48x + 30y = 210

    12x = 30

    cinnamon = 2 1/2 dollars per pound

    spice = 3 dollars per pound

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