Question

11 12 13 14 15 16 17 18 19 20 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

X= price of hotdog
y= price of hamburger

Set up equations for each stand. Multiply number of hotdogs and hamburgers sold by their prices (x and y) and add together to equal the total sold at each stand.


FIRST CONCESSION STAND
164x + 74y= $706

SECOND CONCESSION STAND
256x + 61y= $884


STEP 1
to solve by elimination, multiply first concession stand equation by 61; this will eliminate the y term

164x + 74y= $706
(61)(164x) + (61)(74y)= (61)(706)

10,004x + 4,514y= 43,066


STEP 2
multiply second concession stand equation by -74

256x + 61y= $884
(-74)(256x) + (-74)(61y)= (-74)($884)

-18,944x - 4,514y= -65,416


STEP 3
add step 1 & 2 equations together to solve for x

10,004x + 4,514y= 43,066
-18,944x - 4,514y= -65,416
y terms "cancel out"

-8,940x= -22,350
divide both sides by -8,940

x= $2.50 hotdog


ANSWER: $2.50 is the price of a hotdog.

Hope this helps! :)