A new cruise ship line has just launched 3 new ships: the Pacific, the Caribbean, and the Mediterranean. The Caribbean has 15 more deluxe staterooms than the Pacific. The Mediterranean has 26 fewer deluxe staterooms than four times the 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 805.
Let P = the Pacific
P + P + 15 + 4P - 26 = 805
6P - 11 = 805
6P = 816
P = 136
Let's assume the number of deluxe staterooms on the Pacific is represented by 'P'.
According to the given information, the Caribbean has 15 more deluxe staterooms than the Pacific. Therefore, the number of deluxe staterooms on the Caribbean is 'P + 15'.
The Mediterranean has 26 fewer deluxe staterooms than four times the number of deluxe staterooms on the Pacific. Therefore, the number of deluxe staterooms on the Mediterranean is '4P - 26'.
The total number of deluxe staterooms for the three ships is given as 805. So, the equation representing this information is:
P + (P + 15) + (4P - 26) = 805
To find the number of deluxe staterooms for each ship, we can solve this equation.
Combining like terms, the equation becomes:
6P - 11 = 805
Adding 11 to both sides of the equation:
6P = 816
Dividing both sides of the equation by 6:
P = 136
Now, we have the number of deluxe staterooms on the Pacific, which is 136.
The number of deluxe staterooms on the Caribbean is 'P + 15' = 136 + 15 = 151.
The number of deluxe staterooms on the Mediterranean is '4P - 26' = 4(136) - 26 = 540 - 26 = 514.
Therefore, the number of deluxe staterooms for each ship is as follows:
Pacific: 136
Caribbean: 151
Mediterranean: 514