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?

Phoebe 2021-09-11 Answered
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?
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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(1)

120x+90y=6150(2)
Now,
[120·Equation (1)]−[Equation (2)]

120(x+y)(120x+90y)=120(55)6150120x+120y120x90y=6600615030y=450

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

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