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

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