Alocal hamburger shop sold a combined total of 496 hamburgers and cheeseburgers on thursday. there were 54 fewer cheeseburgers sold than hamburgers. how many hamburgers were sold on thursday?

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If you know the total and how many less/more of one over the other, you just need to assign variables to each. 

Let h = hamburgers; c = cheeseburgers

c + h = 496
c = h - 54
h + (h - 54) = 496
2h = 550
h = 275

c = 275 - 54
c - 221

Verify: 275 + 221 = 496