Expert: Scott A Wilson - 2/9/2011

Question
A new cruise ship line has just launched 3 new ships:the pacific paradise, the Caribbean paradise, and the mediteranean paradise. The Carribean has 16 more deluxe staterooms than the Pacific paradise. The mediteranean has 28 fewer deluxe staterooms than four times the number of deluxe staterooms on the pacific paradise. I need help to find the number of deluxe staterooms for each of the ships if the total number of deluxe staterooms for the 3 ships is 828?

Answer
Let the Pacific Paradise have X deluxe staterooms.
From this, it is known that the Carabbean Paradise has X + 16.
The Mediteranean Paradise has 4X - 28.

Adding the number of staterooms together gives X + X + 16 + 4X - 28.
Now combining terms, there are 3 X's, so we get 6X.
Since 16 - 28 = -12, the whole expression is 6X - 12.

Since we know the total deluxe staterooms is 828, and this is 5X - 12,
we can set 828 = 6X - 12.

To finish this off, add 12 to both sides and get 840 = 6X.
Since 14*6 = 84, and 840 has an extra 0, it must be X = 140.

This is the number of the Pacific Paradise.
To the the number on the Caribean Paradise, add 16 to 140 and get 156.

To get the number on the Mediteranean Paradise, compute 4X - 28 = 4(140) - 4(7) =
4(140-7) = 4(133) = 532

Now if we combine all of the ships to check  this, we get 140 + 156 + 532.
Since 140 + 156 = 296, add this to 532.  Since 296 is 300-4, it would be 532+300-4,
and that is just 832-4 = 828.