Question

A merchant mixed 8 lb of a cinnamon tea with 6 lb of spice tea. The 14-pound mixture cost $38. 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.

Answer 1

The cost of cinnamon tea per pound is $2.5

The cost of spice tea per pound is $ 3

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

-------------------------

`y = (6)/(2)`

y = 3

On substituting y value in eq(1)

8x + 6(3) = 38

8 x + 18 = 38

8x = 38 -18

8x = 20

`x = ( 20)/(8)`

x = 2.5