Let

h = the number of hamburgers sold, h>0

c = the number of cheeseburgers sold, c>0

A local hamburger shop sold a combined total of 384 hamburgers and cheeseburgers on Monday:

h + c = 384

There were 66 fewer cheeseburgers sold than hamburgers:

c = h - 66

We have the system:

h + c = 384

c = h - 66

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h = 225 hamburgers

c = 159 cheeseburgers

There were 225 hamburgers sold on Monday.