Answer to Question #13807 in Algebra for Karla
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.
C = P + 12 = 103 + 12 = 115
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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