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