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?

Question

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,
$x + y = 55 \to (1)$

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

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

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