What is the cost per pound of the cinnamon tea and of the spice tea.

Question

A merchant mixed 10 lb of a cinnamon tea with 2 lb of spice tea. The 12-pound mixture cost $19. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $37. Find the cost per pound of the cinnamon tea and of the spice tea.

Answer 1

Let's assume:

C is Cinnamon Tea and

S is Spice Tea.

The problem gives us two scenarios. We write the scenarios as equations

10 C+ 2 S = 19 (eq 1)

14 C + 8 S = 37 (eq 2)

solving for C in eq 1:

C = (19 - 2S)/10

plug in C into the unused equation (eq 2):

14 ((19-2S)/10)) +8S = 37

Simplifying the above:

26.6 - 2.8S + 8S = 37

Combining like terms:

5.2S=10.4

Solving for S:

S = 2

Solving for C by plugging in S into any of the equations. I choose eq 1.

10C + 2 (2) = 19

10C = 15

C=15/10

C=1.5

Plug into original equation to make sure both sides are equal:

14 C + 8 S = 37

14 (1.5) + 8 (2) = 37

37=37

Since the solutions were able to solve the equation, this means the values are correct.