She earns 9 points per library and 13 points per museum.
Explanation
Lets assume, she earns [tex]x[/tex] point per library.
As she earns 4 more points per museum than per library, so the point earned per museum will be: [tex]x+4[/tex]
She earned total 179 points for building 11 museums and 4 libraries. So, the equation will be...
[tex]11(x+4)+4(x) =179\\ \\ 11x+44+4x=179\\ \\ 15x+44=179\\ \\ 15x=179-44=135\\ \\ x=\frac{135}{15}=9[/tex]
So, she earns 9 points per library and earns (9+4)= 13 points per museum.
