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?

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