# 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

### 3 Answers

- PhilipLv 66 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.

- KrishnamurthyLv 76 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