Algebraic word problem

Mathematics
Tutor: None Selected Time limit: 1 Day

A new cruise line has just launched 3 new ships; the Pacific Paradise, the Caribbean paradise , and the Mediterranean paradise. The Caribbean paradise has 34 more deluxe staterooms than the pacific paradise. The Mediterranean paradise has 48 fewer deluxe staterooms than four times the number of deluxe staterooms on the pacific paradise. Find the number of deluxe staterooms for each of the ships if the total number of staterooms for the 3 ships is 903. 

May 12th, 2015

Let the number of deluxe rooms in pacific paradise be x .


The Caribbean paradise has 34 more deluxe staterooms than the pacific paradise.

So, number of deluxe rooms in caribbean paradise = x + 34


The Mediterranean paradise has 48 fewer deluxe staterooms than four times the number of deluxe staterooms on the pacific paradise.

So, number of deluxe rooms in mediterranean paradise = 4x - 48


The total number of staterooms for the 3 ships is 903. 

So,

x + (x + 34) + (4x - 48) = 903

x + x + 34 + 4x - 48 = 903

6x  - 14 = 903

6x = 903 + 14

6x = 917

x = 917/6

x =  152.8 (Something is wrong with the question. Please check)


There seems to be some mistake in the question. I am getting the number of deluxe rooms as a decimal number. Please check once more. I shall solve based on your response.

May 12th, 2015

The original # of rooms for the carribean is supposed to be 24. I also need the number of rooms for each type of room in my answer

May 12th, 2015

Thank you for the quick response.

But, are these 3 points mentioned in the question correct? 

The Caribbean paradise has 34 more deluxe staterooms than the pacific paradise.

The Mediterranean paradise has 48 fewer deluxe staterooms than four times the number of deluxe staterooms on the pacific paradise

The total number of deluxe rooms for the 3 ships is 903. 

Please post the question once more after checking.

May 12th, 2015

Caribbean paradise should be 24 not 34. Meditteranean is 38 fewer not 48. Sorry, typing error.

May 12th, 2015

Ok. Can you check this also

The total number of deluxe rooms for the 3 ships is 903.

May 12th, 2015

its 904. I dont know what happened. Im so sorry 


May 12th, 2015

Please be a little more careful next time :) 
I shall now post the complete solution.

May 12th, 2015

k. thank you

May 12th, 2015

Let the number of deluxe rooms in pacific paradise be x .

The Caribbean paradise has 24 more deluxe staterooms than the pacific paradise.

So, number of deluxe rooms in caribbean paradise = x + 24

The Mediterranean paradise has 48 fewer deluxe staterooms than four times the number of deluxe staterooms on the pacific paradise.

So, number of deluxe rooms in mediterranean paradise = 4x - 38

The total number of deluxe rooms for the 3 ships is 904. 

So,

x + (x +24) + (4x - 38) = 904

x + x + 24 + 4x - 38 = 904

6x - 14 = 904

6x = 904 + 14

6x = 918

x = 918/6

x = 153


So, number of rooms in the Pacific Paradise = x = 153

Number of rooms in the Caribbean Paradise = x + 24 = 153 + 24 = 177

Number of rooms in the Mediterranean Paradise = 4x - 38 = 4*153 - 38 = 574


May 12th, 2015

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