Answer to Question #5049 in Abstract Algebra for Gabi
Pacific Paradise - P rooms
Caribbean Paradise - C rooms
Mediterranean Paradise - M rooms
Let's formalize the problem statements now:
The caribbean paradise has 27 more deluxe staterooms than the Pacific Paradise, so
C = P + 27.
The Mediterranean Paradise has 32 fewer deluxe staterooms than four times the number of deluxe staterooms of the pacific paradise, so
M = 4P - 32.
At last, the total number of deluxe staterooms for the three ships is 1153, so
P + C + M = 1153.
Here we got the system of equations:
C = P + 27,& (1)
M = 4P - 32,& (2)
P + C + M = 1153. (3)
Let's solve it.
substituting C from (1) and M from (2) to (3) we obtain:
P + P + 27 + 4P - 32 = 1153
6P = 1158
P = 193.
C = P + 27 = 193 + 27 = 220
M = 4P - 32 = 4*193 - 32 = 740.
So, Pacific Paradise has 193 rooms, Caribbean Paradise 220 rooms and Mediterranean Paradise 740 rooms.
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