algebra word problem

Question

Room Prices Ten rooms are rented at rates of $80 and $120 per night. The total collected for the 10 rooms is $920. (a) Write a system of linear equations whose solution gives the number of each type of room rented. Be sure to state what each variable represents. (b) Solve the system of equations.

Answer 1

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.

Answer 2

80x^2 + 120x + 45