Question

Please help..
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?

Answer 1

164x+74y=706
256x+61y=884

Answer 2

This can be solved by setting up equations representing the two stands - if D is the price of a hot dog and H the price of a hamburger, then we know that:

706 = 164D + 74H, and
884 = 256D + 61H

There are a number of ways to proceed from here, but one is to rearrange both equations so they are in the form H = ...., as follows, which will allow us to eliminate H from the equations:

H = (706 - 164D)/74, and
H = (884 - 256D)/61

These two are equal to eachother, so

(706 - 164D/74 = (884 - 256D)/61

Rearranging the equations again, expanding the brackets, and putting all the H's on one side of the equals sign, you get:

61 * (706-164D) = 74 * (884-256D)
43,066 - 10,004D = 65,416 - 18,944D
65,416 - 43,066 = 18,944D - 10,004D
22,350 = 8,940D
D = 22,350/8,940 = 2.5

So a hot dog costs $2.50

Answer 3

Thank you both! :D