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

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