Answer:
- Pacific Paradise = 198 deluxe staterooms
- Caribbean Paradise = 214 deluxe staterooms
- Mediterranean Paradise = 764 deluxe staterooms
Check: 198+214+764 = 1176 total rooms
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Step-by-step explanation
I'll define these variables:
- p = number of deluxe staterooms on Pacific Paradise
- c = number of deluxe staterooms on Caribbean Paradise
- m = number of staterooms on Mediterranean Paradise
We have these given facts:
- The Caribbean Paradise has 16 more deluxe staterooms than the Pacific Paradise.
- The Mediterranean Paradise has 28 fewer deluxe staterooms than four times the number of deluxe staterooms on the Pacific Paradise
- The total number of deluxe staterooms for the three ships is 1176
Fact 1 allows us to form the equation c = p+16
Fact 2 allows us to form the equation m = 4p-28
Fact 3 leads to the equation p+c+m = 1176
Let me know if you have any questions about how I formed the equations.
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The system of equations is:
Notice how the first two equations have the variable p on the right hand side, and no other variable. We'll use this to apply substitution and solve for p.
p+c+m = 1176
p+(p+16)+m = 1176 ... replace c with p+16
p+(p+16)+(4p-28) = 1176 ... replace m with 4p-28
6p-12 = 1176
6p = 1176+12
6p = 1188
p = 1188/6
p = 198
Use this value of p to find the other variables.
c = p+16 = 198+16 = 214
m = 4p-28 = 4*198-28 = 764
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Summary:
We found that p = 198, c = 214, and m = 764.
- Pacific Paradise = 198 deluxe staterooms
- Caribbean Paradise = 214 deluxe staterooms
- Mediterranean Paradise = 764 deluxe staterooms
As a check,
198+214+764 = 1176 total rooms
The answer is confirmed.