SOLUTION: A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18 pound mixture cost $39. A second mixture included 16 lb of the cinnamon tea and 10 lb of the spice tea. The

Algebra ->  Equations -> SOLUTION: A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18 pound mixture cost $39. A second mixture included 16 lb of the cinnamon tea and 10 lb of the spice tea. The       Log On


   

Question 715521: A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18 pound mixture cost $39. A second mixture included 16 lb of the cinnamon tea and 10 lb of the spice tea. The 26 pound mixture cost $57. Find the cost per pound of the cinnamon tea and of the spice tea.
$_____ per lb cinnamon
$_____ per lb spice
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Price of the cinnamon tea $/# = c
Price of the spice tea, $/# = s

Mixture Size 18 Pounds
Amount Cinn___________12#
Amount Spice__________6#
Mixture Cost__________39$
Equation for Cost_____12*c+6*s=39

Mixture Size 26 Pounds
Amount Cinn___________16#
Amount Spice__________10#
Mixture Cost__________57$
Equation for Cost_____16*c+10*s=57

INITIALLY THE SYSTEM TO SOLVE:
12%2Ac%2B6%2As=39
16%2Ac%2B10%2As=57
The $39 equation can be simplified, dividing by 3.
The $39 equation is the same as 4c%2B2s=13.

A BETTER SYSTEM:
highlight%284c%2B2s=13%29
highlight%2816c%2B10s=57%29

The easiest next step is to multiply the "13" equation by 4 which will allow you to eliminate terms of x and solve for s, its value. I leave that advice and the rest of the solution for you to finish (or to comment on if you get stuck).