SOLUTION: During a football game, a concession stand sold a family 3 hamburgers and 2 hotdogs for a total of $13. It sold another family 2 hamburgers and 5 hotdogs for a total of $16. What a

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: During a football game, a concession stand sold a family 3 hamburgers and 2 hotdogs for a total of $13. It sold another family 2 hamburgers and 5 hotdogs for a total of $16. What a      Log On


   

Question 1012761: During a football game, a concession stand sold a family 3 hamburgers and 2 hotdogs for a total of $13. It sold another family 2 hamburgers and 5 hotdogs for a total of $16. What are the prices of a hamburger and hotdog??
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Call the prices of hamburger and hot dogs, x and y. Then we can write
3x + 2y = 13 and
2x + 5y = 16
Multiply the top by two and the bottom one by three and subtract...we get
6x + 4y = 26
-(6x + 15y = 48)
-------------------
-11y = -22
y = 2 dollars per hot dog
Then
3x + 2(2) = 13
3x + 4 = 13
3x = 9
x = 3 dollars per burger