Let x be the number of $80 rooms rented.
Let y be the number of $120 rooms rented.
We have:
x + y = 10 --- (1)
80x + 120y = 920 --- (2)
From (1), we have:
y = 10 - x --- (3)
Substituting (3) into (2), we will get:
80x + 120(10 - x) = 920
80x + 1200 - 120x = 920
120x - 80x = 1200 - 920
40x = 280
x = 280 / 40
x = 7
Substituting x = 7 into (3), we will get:
y = 10 - 7
y = 3
Hence, seven $80 rooms and three $120 rooms were rented.