SOLUTION: A group of students bought 10 barbecues and 12 soft drinks at a price of $360. Another group bought 5 barbecues and 6 softdrinks at a price of $120. What is the price of a single

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A group of students bought 10 barbecues and 12 soft drinks at a price of $360. Another group bought 5 barbecues and 6 softdrinks at a price of $120. What is the price of a single      Log On


   

Question 942589: A group of students bought 10 barbecues and 12 soft drinks at a price of $360.
Another group bought 5 barbecues and 6 softdrinks at a price of $120. What is the price of a single barbecue and softdrink?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

barbecues x
soft drinks y
if a group of students bought 10 barbecues and 12 soft drinks at a price of $360, then we have
10x%2B12y=360.........eq.1
and another group bought 5 barbecues and 6 soft-drinks at a price of $120, we have

5x%2B6y=120.........eq.2


solve the system:
10x%2B12y=360.........eq.1
5x%2B6y=120.........eq.2
----------------------------------subtract 2 from 1
10x%2B12y-5x%2B6y=360-120
5x%2B6y=240
5x=240-6y
x=%28240-6y%29%2F5 ....substitute in 2
5%28240-6y%29%2F5%2B6y=120.........eq.2
240-6y%2B6y=120...since -6y%2B6y=0
240%3C%3E120 => lines are parallel and there is no solution; this system is inconsistent
10x%2B12y=360.........eq.1
5x%2B6y=120.
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+50%2C+-10x%2F12%2B36%2C+-5x%2F6%2B20%29+
so, we cannot determine what is the price of a single barbecue and soft-drink