Answer to Question #5049 in Abstract Algebra for Gabi

Question

A new cruise ship line has just launched 3 new ships: The pacific paradise, the Caribbean Paradise, and the Mediterranean Paradise. The caribbean paradise has 27 more deluxe staterooms than the Pacific Paradise.The Mediterranean Paradise has 32 fewer deluxe staterooms than four times the number of deluxe staterooms of 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 is 1153

Answer 1

Let's make such denotations:
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.

Then,
C = P + 27 = 193 + 27 = 220
and
M = 4P - 32 = 4*193 - 32 = 740.

So, Pacific Paradise has 193 rooms, Caribbean Paradise 220 rooms and Mediterranean Paradise 740 rooms.