She earns 9 points per library and 13 points per museum.
Step-by-step explanation
Lets assume, she earns
point per library.
As she earns 4 more points per museum than per library, so the point earned per museum will be:

She earned total 179 points for building 11 museums and 4 libraries. So, the equation will be...

So, she earns 9 points per library and earns (9+4)= 13 points per museum.