# Answer to Question #15175 in Abstract Algebra for Brittany

Question #15175

A new cruise ship line has just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise, and the Mediterranean Paradise. The Caribbean Paradise has 33 more deluxe staterooms that the Pacific Paradise. The Mediterranean Paradise has 36 fewer deluxe staterooms that 4 times the number of deluxe staterooms on the Pacific Paradise. Find the number of deluxe staterooms for each of the ships if the total numbers of deluxe staterooms for the three ships is 837.

Expert's answer

Let's make such denotations:

Pacific Paradise - P rooms

Caribbean Paradise - C rooms

Mediterranean Paradise - M rooms

Let's formalize the problem statements now:

The caribbean paradise has 33 more deluxe staterooms than the Pacific Paradise, so

C = P + 33.

The Mediterranean Paradise has 36 fewer deluxe staterooms than four times the number of deluxe staterooms of the pacific paradise, so

M = 4P - 36.

At last, the total number of deluxe staterooms for the three ships is 837, so

P + C + M = 837.

Here we got the system of equations:

C = P + 33,& (1)

M = 4P - 36,& (2)

P + C + M = 837. (3)

Let's solve it.

substituting C from (1) and M from (2) to (3) we obtain:

P + P + 33 + 4P - 36 = 837 ==> 6P = 840 ==> P = 140.

Then,

C = P + 33 = 140 + 32 = 172

and

M = 4P - 36 = 4*140 - 36 = 524.

So, Pacific Paradise has 140 rooms, Caribbean Paradise 172 rooms and Mediterranean Paradise 524 rooms.

Pacific Paradise - P rooms

Caribbean Paradise - C rooms

Mediterranean Paradise - M rooms

Let's formalize the problem statements now:

The caribbean paradise has 33 more deluxe staterooms than the Pacific Paradise, so

C = P + 33.

The Mediterranean Paradise has 36 fewer deluxe staterooms than four times the number of deluxe staterooms of the pacific paradise, so

M = 4P - 36.

At last, the total number of deluxe staterooms for the three ships is 837, so

P + C + M = 837.

Here we got the system of equations:

C = P + 33,& (1)

M = 4P - 36,& (2)

P + C + M = 837. (3)

Let's solve it.

substituting C from (1) and M from (2) to (3) we obtain:

P + P + 33 + 4P - 36 = 837 ==> 6P = 840 ==> P = 140.

Then,

C = P + 33 = 140 + 32 = 172

and

M = 4P - 36 = 4*140 - 36 = 524.

So, Pacific Paradise has 140 rooms, Caribbean Paradise 172 rooms and Mediterranean Paradise 524 rooms.

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