At a concession stand, seven hot dog (s) and four hamburger (s) cost $15.75 ; four hot dog (s) and seven hamburger (s) cost $17.25. Find the cost of one hot dog and the cost of one hamburger.

The answer is: Each hot dog costs $1.25 and each hamburger costs $1.75

Explanation:

D = hot dog and H = hamburger

(7D + 4H = $15.75) x 7

(4D + 7H = $17.25) x - 4

We multiply:

49D + 28H = $110.25

-16D - 28H = - $69

We add both equations:

(49D - 16D) + (28H - 28H) = $110.25 - $69

33D = $41.25

D = $41.25 / 33 = $1.25

Then we replace D with $1.25

(7 x $1.25) + 4H = $15.75

4H + $8.75 = $15.75

4H = $7

H = $1.75