A new cruise ship line has just launched 3 new ships: the Pacific Paradise, the caribbean paradise, and the mediterranean paradise. The carabbean paradise has 19 more deluxe staterooms than the Pacific paradise. The mediterranean paradise has 36 fewer duluxe rooms than twice the number of the deluxe rooms on the pacific paradise. find the number of deluxe rooms for each of the ships if the total number of deluxe rooms for the three ships is 399

Let P = x, then C = x +19 and M = 2x - 36

x + (x+19) + (2x-36) = 399

Calculate x, then the others.

To solve this problem, let's assign variables to the unknown quantities:

Let's say the number of deluxe rooms on the Pacific Paradise is x.

According to the problem, the Caribbean Paradise has 19 more deluxe rooms than the Pacific Paradise. So, the number of deluxe rooms on the Caribbean Paradise is x + 19.

The problem also states that the Mediterranean Paradise has 36 fewer deluxe rooms than twice the number of deluxe rooms on the Pacific Paradise. So, the number of deluxe rooms on the Mediterranean Paradise is (2x) - 36.

We know that the total number of deluxe rooms for the three ships is 399. Therefore, we can set up the equation:

x + (x + 19) + (2x - 36) = 399

Now, let's solve for x:

4x - 17 = 399

Adding 17 to both sides of the equation:

4x = 416

Dividing both sides by 4:

x = 104

Therefore, the Pacific Paradise has 104 deluxe rooms.

Now let's find the deluxe room numbers for the other two ships:

Caribbean Paradise: x + 19 = 104 + 19 = 123

Mediterranean Paradise: (2x) - 36 = (2 * 104) - 36 = 208 - 36 = 172

So, the number of deluxe rooms for each ship is as follows:

Pacific Paradise: 104 rooms
Caribbean Paradise: 123 rooms
Mediterranean Paradise: 172 rooms