Question

A hotel offers single rooms for $90 a night and suites for $150 a night. One night, a clerk notes that a total of 24 rooms were sold but did not write down how many of each type were sold. If the hotel charged a total of $2,520, then how many of each type of room were sold?


If the hotel made a total of $2,520 that night, then how many of the rooms sold were suites?

How many were Single rooms?

Answer 1

There were 18 single rooms and 6 suites booked.

Step-by-step explanation:

Given,

Cost of one single room = $90

Cost of one suite = $150

Total rooms booked = 24

Total amount earned = $2520

Let,

Number of single rooms = x

Number of suite = y

According to given statement;

x+y=24     Eqn 1

90x+150y=2520    Eqn 2

Multiplying Eqn 1 by 90

$90(x+y=24)\\90x+90y=2160\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(90x+150y)-(90x+90y)=2520-2160\\90x+150y-90x-90y=360\\60y=360$

Dividing both sides by 60

$\frac{60y}{60}=\frac{360}{60}\\y=6$

Putting y=6 in Eqn 1

$x+6=24\\x=24-6\\x=18$

There were 18 single rooms and 6 suites booked.

Keywords: linear equation, variable

Learn more about variables at:

• brainly.com/question/10978510
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