Question

The caribbean paradise has 10 more rooms than the pacific paradise. The mediterranean paradise has 13 fewer rooms than 4 times the number of rooms on the pacific paradise. find the number of rooms if the total of room is 843.

Answer 1

The caribbean paradise has 10 more rooms than the pacific paradise:\[C=P+10\]
The mediterranean paradise has 13 fewer rooms than 4 times the number of rooms on the pacific paradise:\[M=4P-13\]
total of room is 843:\[C+P+M=843\]

Answer 2

substitute the first two equations in the 3rd:
\[\left( P+10 \right)+P+\left( 4P-13 \right)=843\]\[\implies 6P-3=843\]\[\implies 6P=846\]
\[\implies \Large P = 141\]\[\implies \Large C = 151\]\[\implies {\Large M} = 4\times141-13=564-13\Large=551\]