A hamburger costs 30¢ more than a hot dog and 20¢ less than a cheeseburger. If 3 hamburgers cost 75¢ less than 2 hot dogs and 2 cheeseburgers, how much does a
hamburger cost?

Let h be the price of a hamburger, d be the price of a hot dog and c be the price of a cheeseburger
3+d=h —(1)
c-20=h —(2)
3h=2d+2c-75 —(3)

Sub (1), (2) into (3)
3h=2(h-3) + 2(h+20) -75
3h =2h-6+2h+40-75
3h=4h-41
h=41

Therefore, the price of a hamburger is $41

The price of the hamburger is 41