word problems

Question

A merchant mixed 12 lb of a cinnamon tea with 4 lb of spice tea. The 16-pound mixture cost $26. A second mixture included 16 lb of the cinnamon tea and 6 lb of the spice tea. The 22-pound mixture cost $36. Find the cost per pound of the cinnamon tea and of the spice tea.

Answer 1

Let C = Cinnamon, S = Spice

Given: 

12C + 4S = 26

16C + 6S = 36

 

Multiply 1st equation by 3, and multiply 2nd equation by 2....you will have 12S for both equations:

36C + 12S = 78 --> 12S = 78 - 36C

32C + 12S = 72 --> 12S = 72 - 32C

 

Set the two equations equal to each other

78 - 36C = 72 - 32C

Minus 72 on both side, and add 36C on both side

6 = 4C

C = 6/4 or 3/2 or $1.50

 

Plug C back into one of the original equation to solve for S

12C + 4S = 26

12(1.5) + 4S = 26

18 + 4S = 26

4S = 8

S = 2 or $2.00