At a concession stand, five hot dog(s) and two hamburger(s) cost $\$10.25$; two hot dog(s) and five hamburger(s) cost $\$12.50$. Find the cost of one hot dog and the cost of one hamburger.
Let the cost of a hot dog be x and the cost of a hamburger be y. We can write a system of equations:
5x + 2y = 10.25
2x + 5y = 12.50
Add both equations:
7x + 7y = 22.75
x + y = 22.75/7 = $3.25