a new cruise line has just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise and the Mediterranean Paradise. The Caribbean has 32 more deluxe staterooms than the Pacific. The Mediterranean has 36 fewer deluxe staterooms than four times a number of deluxe staterooms on the Pacific. Find the number of deluxe staterooms for each of the ships if the total number of deluxe staterooms for the three ships is 872.
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 32 more deluxe staterooms than the Pacific Paradise, so
C = P + 32.
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 872, so
P + C + M = 872.
Here we got the system of equations:
C = P + 32,& (1) M = 4P - 36,& (2) P + C + M = 872. (3)
Let's solve it. substituting C from (1) and M from (2) to (3) we obtain: P + P + 32 + 4P - 36 = 872 ==> 6P = 876 ==> P = 146.
Then, C = P + 32 = 146 + 32 = 178 and M = 4P - 36 = 4*146 - 36 = 548.
So, Pacific Paradise has 146 rooms, Caribbean Paradise 178 rooms and Mediterranean Paradise 548 rooms.