# A motel in a suburb of Chicago rents double rooms for $120 per day and single rooms for$90 per day.how many of each kind were rented?

solve each problem by setting up and solving an appropriate system of equations.
A motel in a suburb of Chicago rents double rooms for $120 per day and single rooms for$90 per day. If a total of 55 rooms were rented for $6150, how many of each kind were rented? You can still ask an expert for help Expert Community at Your Service • Live experts 24/7 • Questions are typically answered in as fast as 30 minutes • Personalized clear answers Solve your problem for the price of one coffee • Available 24/7 • Math expert for every subject • Pay only if we can solve it ## Expert Answer Arnold Odonnell Answered 2021-09-12 Author has 109 answers A motel in a suburb of Chicago rents double rooms for$120 per day and single rooms for $90 per day and total of 55 rooms were rented for$6150.
Let x & y be the number of double rooms and single rooms respectively. Then,
$x+y=55\to \left(1\right)$

$120x+90y=6150\to \left(2\right)$
Now,
[120·Equation (1)]−[Equation (2)]

$⇒120\left(x+y\right)$$-\left(120x+90y\right)=120\left(55\right)-6150⇒120x+120y-120x-90y=6600-6150⇒30y=450$

$⇒y=15$
Now put $y=15$ in equation (1), we get
$⇒x+15=55⇒x=40$
Hence 40 double rooms and 15 single rooms were rented.