Marty's road-side grill sells hot dogs for $1.25 and hamburgers for $2.50. during a busy summer weekend, he sells a total of 177 hot dogs and hamburgers combined for $363.75. how many hot dogs did he sell? how many hamburgers?

We have to create system of equation
Assume x - number of hot dogs, y - number of hamburgers
We have

From first equation we get
y+x=177   /-x
y=177-x      
Now we can substitute to second eq
1.25x+2.5y=363.75
1.25x+2.5*(177-x)=363.75
1.25x+442.5-2.5x=363.75
-1.25x+442.5=363.75     /-442.5
-1,25x=-78.75            /:(-1.25) divide both sides by -1.25
x=63

Now we can back substitute
y=177-63
y=114
Finally we have

So sold 117 hamburgers and 63 hotdogs