Find the cost per pound of the cinnamon tea and of the spice tea.

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

Let x represent cost per pound of cinnamon tea

Let y represent cost per pound of spice tea

From the first two sentences we get that 38 = 8x + 6y

The next two sentences give us 70 = 16x + 10y

I am going to alter the first equation in order to isolate y, from there we can substitute it into the second equation.

38 = 8x + 6y

38 - 8x = 6y

19/3 - 4x/3 = y

I will now plug this equation for y into my second equation and solve for x.

70 = 16x + 10(19/3 - 4x/3)

70 = 16x + 190/3 - 40x/3

70 = 8x/3 + 190/3

20/3 = 8x/3

20 = 8x

5/2 or 2.5 = x