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Answer to Question #13807 in Algebra for Karla

Question #13807
A new cruise ship line has launched 3 new ships: the pacific paradise, the Caribbean paradise, and the Mediterranean paradise. The Caribbean paradise has 12 more deluxe staterooms than the pacific paradise. The Mediterranean paradise has 16 fewer deluxe staterooms than three times the number of deluxe staterooms on the pacific paradise. Find the number of deluxe staterooms for each of the ships if the total number of deluxe staterooms for the three ships 511.
Expert's answer
Let's make such denotions:
Pacific Paradise - P rooms
Caribbean Paradise - C rooms
Mediterranean Paradise - M rooms

Let's formalize the problem statements now:

The caribbean paradise has 12 more deluxe staterooms than the Pacific Paradise, so

C = P + 12.

The Mediterranean Paradise has 16 fewer deluxe staterooms than three times the number of deluxe staterooms of the pacific paradise, so

M = 3P - 16.

At last, the total number of deluxe staterooms for the three ships is 511, so

P + C + M = 511.

Here we got the system of equations:

C = P + 12,& (1)
M = 3P - 16,& (2)
P + C + M = 511. (3)

Let's solve it.
substituting C from (1) and M from (2) to (3) we obtain:
P + P + 12 + 3P - 16 = 511 ==> 5P = 515 ==> P = 103.

Then,
C = P + 12 = 103 + 12 = 115
and
M = 3P - 16 = 3*103 - 16 = 293.

So, Pacific Paradise has 103 rooms, Caribbean Paradise 115 rooms and Mediterranean Paradise 293 rooms.

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