Question 892101
c = count of rooms for Caribbean Paradise
p = rooms for Pacific
m = rooms for Mediterranean


{{{c=12+p}}};
{{{m=-15+p}}};
{{{c+p+m=525}}}.


The c and m equations:
p=c-12 and p=m+15
{{{c-12=m+15}}}
{{{c-m=15+12}}}
{{{highlight_green(c-m=27)}}}


Substitute for p in the "525" equation:
{{{c+(m+15)+m=525}}}-----( the equation p=c-12 could have been used instead )
{{{c+2m+15=525}}}
{{{highlight_green(c+2m=510)}}}


Use those two green-outlined equations.
{{{c+2m-(c-m)=510-27}}} -------using Elimination Method to handle this part
{{{3m=483}}}
{{{m=483/3}}}
{{{highlight(m=161)}}}
This is one part of the solution.
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Use m to find the values for p and c.


This problem could be handled in many ways.  You could also use matrices.