Question

a concession stand is selling hot dogs and hamburgers during a game. at halftime they sold a total of 78 hot dogs and hamburgers and brought in $105.50. how many of each item did they sell if hamburgers sold for $1.50 and hot dogs sold for $1.25?

Answer 1

Let x=number of hamburgers sold and y=number of hot dogs sold.
Step 1)
cost of burgers X # of burgers + cost of hotdogs X # of hotdogs=$ collected               1.5x + 1.25y=105.5

step 2)
# of burgers sold + number of hot dogs sold = total number of items sold
     x + y = 78

step 3)  solve for y in the second equation
     y = 78 - x

step 4)  substitute y = 78 - x in the first equation for the value of y and solve for x
     1.5x + 1.25(78 - x)=105.50
     1.5 x + 97.5 - 1.25x=105.50
     .25x = 8
     x = 32


step 5)  plug in our value for x in the second equation and solve for y
     x+y=78
     32+y=78
     y=46

answer       32 hamburgers and 46 hot dogs