Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands. at their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers. if the prices are the same at both concession stands, what is the price of a hot dog?

We have to solve the system of equations ( x  - the price of hot dog, y - the price of hamburgers ):164 x + 74 y = 706  / : 2  ( we have to divide both sides of equation by 2 )256 x + 61 y = 88482 x + 37 y = 353        /  * ( - 61 )
256 x + 61 y = 884      / * 37 5,002 x - 2,257 y = - 21,533+
  9,472 x +2,257 y =   32,708 4,470 x = 11,175x = 11,175 : 4,470x = 2.5 The price of hot dog is $2.5.

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