80 rooms with kitchen facility and 120 rooms without kitchen facility were rented.
Step-by-step explanation:
Given,
Total rooms = 200
Cost of kitchen facility rooms = $300 per night
Cost of without kitchen facility rooms = $180 per night
Total collected = $45600
Let,
x be the number of kitchen facility rooms.
y be the number of without kitchen facility rooms.
According to given statement;
x+y=200 Eqn 1
300x+180y=45600 Eqn 2
From Eqn 1
x=200-y Eqn 3
Putting value of x from Eqn 3 in Eqn 2
[tex]300(200-y)+180y=45600\\60000-300y+180y=45600\\-120y=45600-60000\\-120y=-14400\\[/tex]
Dividing both sides by -120
[tex]\frac{-120y}{-120}=\frac{-14400}{-120}\\y=120[/tex]
Putting y=120 in Eqn 1
[tex]x+120=200\\x=200-120\\x=80\\[/tex]
80 rooms with kitchen facility and 120 rooms without kitchen facility were rented.
Keywords: linear equations, substitution method
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