Answer to Question #1698 in Algebra for Doug

Question

A new cruise ship line has just launched 3 new ships. The Pacific Paradise, the Caribbean Paradise, & the Mediterranean Paradise. The Caribbean Paradise has 37 more deluxe staterooms than the Pacific Paradise. The Mediterranean Paradise has 40 fewer deluxe staterooms than 4 times the number of deluxe staterooms on the Pacific Paradise. Find the number of deluxe staterooms for each of the ship if the total number of deluxe staterooms for the 3 ships is 819.

Answer 1

Denote the number of deluxe staterooms in Pacific Paradise as x,
as the Caribbean Paradise has 37 more deluxe staterooms than the Pacific Paradise, it would have (x+ 37) staterooms,
as the Mediterranean Paradise has 40 fewer deluxe staterooms than 4 times the number of deluxe staterooms on the Pacific Paradise, it would have (4x - 40) deluxe staterooms.
The total number of staterooms is:
x + x + 37 + 4x - 40 = 819
6x - 3 = 819
6x = 822
x = 137
x + 37 = 174
4x - 40 = 508
Thus the Pacific Paradise has 137 deluxe staterooms, the Caribbean Paradise has 174 deluxe staterooms, the Mediterranean Paradise has 508 deluxe staterooms.