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! :)
