Call the number of hamburgers 'H' and the number of cheeseburgers 'C'.
We are told that:
[tex] C+H=824 [/tex]
and
[tex] C=H+74[/tex]
by back substitution:
[tex]H+74+H=824[/tex] or [tex]2H=750[/tex] thus [tex]H=375[/tex] and so [tex]C=449[/tex]
To check:
[tex]C+H=824[/tex]
[tex]449+375=824[/tex]
[tex]824=824[/tex] CHECKS
