Problema Solution
A new cruise ship line has just launched 3 new ships: the Pacific Paradise, the Carribbean Paradise, and the Mediterranean Paradise. The Carribbean Paradise has 15 more deluxe state rooms than the Pacific Paradise. The Mediterranean Paradise has 16 fewer deluxe state rooms than twice the number of deluxe state rooms on the Pacific Paradise. Find the number of deluxe state rooms for each of the ships if the total number of deluxe state rooms for the three ships is 555.
Answer provided by our tutors
Let C = staterooms on Caribbean, M = staterooms on Mediterranean, P = staterooms on paradise
"The Caribbean paradise has 11 more deluxe staterooms than the pacific paradise."
C = P + 11 ... ... ... (Eq1)
"The Mediterranean paradise has 39 fewer deluxe staterooms than four times the number of deluxe staterooms on the pacific paradise."
M = 4P - 39 ... ... ... (Eq2)
"the total number of deluxe staterooms for the three ships is 692"
C + M + P = 692 ... ... ... (Eq3)
Now substitute equations 1 and 2 into equation 3:
(P + 11) + (4P - 39) + P = 692
6P - 28 = 692
6P = 720
P = 120
Now recall Eq1:
C = P + 11 = 120 + 11 = 131
and Eq2:
M = 4P - 39 = 4 * 120 - 39 = 441
The pacific paradise has 120 Deluxe staterooms
The Caribbean paradise has 131 Deluxe staterooms
The Mediterranean paradise has 441 Deluxe staterooms