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?

The price of a hot dog be $2.41.

Step-by-step explanation:

Let us assume that the price of the hot dogs be x.

Let us assume that the price of the hamburgers  be y.

As given

Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands.

Than the equation becomes

164x + 74y = 706

At their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers.

Than the equation becomes

256x + 61y = 884

Than two equations are

164x + 74y = 706

256x + 61y = 884

Multiply 164x + 74y = 706 by 61 than equation becomes

10004x + 4514y = 43066

Multiply 256x + 61y = 884  by 74 than equation becomes

18944x + 4514y = 65416

Subtracted 10004x + 4514y = 43066 from 18944x + 4514y = 65416 .

18944x - 10004x + 4514y - 4514y = 65416 - 43066

8940x = 22350

x = 2.5 (Approx)

Therefore the price of a hot dog be $2.5 (Approx)