Question #13285

A new cruise ship line has just lainched 3 new ships; the Pacific paradise, the Caribbean paradise, and the Mediterranean paradise. The caribbean paradise has 17 more deluxe staterooms then the pacific paradise. the mediterranean paradise has 19 fewer deluxe staterooms than three times th number of deluxe staterooms on pacific paradise. Find the number of deluxe staterooms for each of the ships if the total number os deluxe staterooms for the three ships is 788. 0

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 17 more deluxe staterooms than the Pacific Paradise, so

C = P + 17.

The Mediterranean Paradise has 19 fewer deluxe staterooms than three times the number of deluxe staterooms of the pacific paradise, so

M = 3P - 19.

At last, the total number of deluxe staterooms for the three ships is 788, so

P + C + M = 788.

Here we got the system of equations:

C = P + 17,& (1)

M = 3P - 19,& (2)

P + C + M = 788. (3)

Let's solve it.

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

P + P + 17 + 3P - 19 = 788 ==> 5P = 790 ==> P = 158.

Then,

C = P + 17 = 158 + 17 = 175

and

M = 3P - 19 = 3*158 - 19 = 455.

So, Pacific Paradise has 158 rooms, Caribbean Paradise 175 rooms and Mediterranean Paradise 455 rooms.

Pacific Paradise - P rooms

Caribbean Paradise - C rooms

Mediterranean Paradise - M rooms

Let's formalize the problem statements now:

The caribbean paradise has 17 more deluxe staterooms than the Pacific Paradise, so

C = P + 17.

The Mediterranean Paradise has 19 fewer deluxe staterooms than three times the number of deluxe staterooms of the pacific paradise, so

M = 3P - 19.

At last, the total number of deluxe staterooms for the three ships is 788, so

P + C + M = 788.

Here we got the system of equations:

C = P + 17,& (1)

M = 3P - 19,& (2)

P + C + M = 788. (3)

Let's solve it.

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

P + P + 17 + 3P - 19 = 788 ==> 5P = 790 ==> P = 158.

Then,

C = P + 17 = 158 + 17 = 175

and

M = 3P - 19 = 3*158 - 19 = 455.

So, Pacific Paradise has 158 rooms, Caribbean Paradise 175 rooms and Mediterranean Paradise 455 rooms.

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