Question

A merchant mixed 12 lb of a cinnamon tea with 3 lb of spice tea. The 15-pound mixture cost $24. A second mixture included 14 lb of the cinnamon tea and 12 lb of the spice tea. The 26-pound mixture cost $45. Find the cost per pound of the cinnamon tea and of the spice tea.

Answer 1

Hey there!!

Let us take the price of cinnamon tea as ' x ' and spice tea as ' y '

Now, let us take it into equation

12x + 3y = 15  -------------- ( 1 )

14x + 12y = 45 --------------- ( 2 )

Let us multiply the first equation with 4

48x + 12y = 60 --------------- ( 1 )

14x + 12y = 45 --------------- ( 2 )

Now, subtract equation 2

48x + 12y = 60

-14x - 12y = -45

Now, we get,

34x = 15

x = 15 / 34

This is the cost for cinnamon tea = $ 15 / 34

Now, substitute this into one equation

Let us take this equation - 12x + 3y = 15  

Now, substitute ' x '

12 ( 15 / 34 ) + 3y = 15

6 ( 15 / 17 ) + 3y = 15

90 / 17 + 3y = 15

3y = 15 - 90/17

3y = 165 / 17

y = ( 165/17 ) ( 1 / 3 )

y = $ 55/17

Cinnamon tea = $ 15/34

Spice tea = $ 55/17

Hope helps!