SOLUTION: there are 53 students accomodation in 21 rooms of a youth hostle. each room has either 2 or 3 beds. assuming that each student sleeps in one bed only and that every bed is used, fi

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: there are 53 students accomodation in 21 rooms of a youth hostle. each room has either 2 or 3 beds. assuming that each student sleeps in one bed only and that every bed is used, fi      Log On


   



Question 935940: there are 53 students accomodation in 21 rooms of a youth hostle. each room has either 2 or 3 beds. assuming that each student sleeps in one bed only and that every bed is used, find out how many rooms with 2 beds and how many rooms with 3 beds are there.

(Hint let x represent the number of rooms with 2 beds and let y represent the number of rooms with 3 beds)
Please give a full detailed answer.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +x+%2B+y+=+21+
(2) +2x+%2B+3y+=+53+
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Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +2x+%2B+3y+=+53+
(1) +-2x+-+2y+=+-42+
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+y+=+11+
and
(1) +x+%2B+y+=+21+
(1) +x+%2B+11+=+21+
(1) +x+=+10+
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There are 10 rooms with 2 beds
There are 11 rooms with 3 beds
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check:
(2) +2x+%2B+3y+=+53+
(2) +2%2A10+%2B+3%2A11+=+53+
(2) +20+%2B+33+=+53+
(2) +53+=+53+
OK