SOLUTION: Page 326 #12. A merchant mixed 10lb. of cinnamon tea with 5lb. of spice tea. The 15-pound mixture cost $4o. A second mixture included 12 lb. of cinnamon tea and 8 lb of spice tea.

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: Page 326 #12. A merchant mixed 10lb. of cinnamon tea with 5lb. of spice tea. The 15-pound mixture cost $4o. A second mixture included 12 lb. of cinnamon tea and 8 lb of spice tea.       Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 52958: Page 326 #12. A merchant mixed 10lb. of cinnamon tea with 5lb. of spice tea. The 15-pound mixture cost $4o. A second mixture included 12 lb. of cinnamon tea and 8 lb of spice tea. The 20-pound mixture cost $54. Find the cost per pound of the cinnamon tea and the spice tea. how do I solve this problem?
Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
I don't have your book, so I'm going to show you one of the first ways a student learns to solve a problem like this. If you need to solve this using matrices, please resubmit your question and indicate that you need to solve this using matrices. In both mixtures let the cost per pound of cinamin tea=x and the cost per pound of spiced tea =y.
For the first mixture:
Let the price of cinamin tea=10x
Let the price of spiced tea=5y
Total:40
First equation:10x+5y=40
For the second mixture:
Let the price of cinamin tea=12x
Let the price of the spiced tea=8y
Total:54
Second equation:12x+8y=54
So the system of eqautions you need to solve:
10x+5y=40
12x+8y=54
--------------------------------------------
8(10x+5y)=8(40)
-5(12x+8y)=-5(54)
--------------------------------------------
80x+40y=320 Add the two equations
-60x-40y=-270
_____________
20x=50
----------------------------------------------
20x/20=50/20
x=2.5
--------------------------------------------
10(2.5)+5y=40 Subtitute x=2.5 into the first equation.
25+5y=40
-25+25+5y=40-25
5y=15
5y/5=15/5
y=3
-------------------------------------------------
The cost per pound of cinamin tea is x=$2.50.
The cost per pound of spiced tea is y=$3.00