Answer:
The cost of cinnamon tea per pound is $2.5
The cost of spice tea per pound is $ 3
Step-by-step explanation:
Let the cost of cinnamon tea per pound be x
Let the cost of spice tea per pound be y
Then according to the question:
A merchant mixed 8 lb of a cinnamon tea with 6 lb of spice tea. and its cost is $38
Then,
8x + 6y = 38-------------------------------(1)
A second mixture included 16 lb of the cinnamon tea and 10 lb of the spice tea. The 26-pound mixture cost $70
16x + 10y = 70----------------------------(2)
To Solving (1) and (2)
Multiply (1) by 2 then
16x + 12y = 76-----------------------------(3)
Subtracting (2) from (3)
16x + 12y = 76
16x + 10y = 70
------------------------
0x + 2y = 6
-------------------------
[tex]y = \frac{6}{2}[/tex]
y = 3
On substituting y value in eq(1)
8x + 6(3) = 38
8 x + 18 = 38
8x = 38 -18
8x = 20
[tex]x = \frac{ 20}{8}[/tex]
x = 2.5
