Answer to Question #15175 in Abstract Algebra for Brittany
Pacific Paradise - P rooms
Caribbean Paradise - C rooms
Mediterranean Paradise - M rooms
Let's formalize the problem statements now:
The caribbean paradise has 33 more deluxe staterooms than the Pacific Paradise, so
C = P + 33.
The Mediterranean Paradise has 36 fewer deluxe staterooms than four times the number of deluxe staterooms of the pacific paradise, so
M = 4P - 36.
At last, the total number of deluxe staterooms for the three ships is 837, so
P + C + M = 837.
Here we got the system of equations:
C = P + 33,& (1)
M = 4P - 36,& (2)
P + C + M = 837. (3)
Let's solve it.
substituting C from (1) and M from (2) to (3) we obtain:
P + P + 33 + 4P - 36 = 837 ==> 6P = 840 ==> P = 140.
C = P + 33 = 140 + 32 = 172
M = 4P - 36 = 4*140 - 36 = 524.
So, Pacific Paradise has 140 rooms, Caribbean Paradise 172 rooms and Mediterranean Paradise 524 rooms.
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