Suppose that Lucy will be $x$ years old $3$ years later, Cathy will be $$(x+23)$$ years old. $x+(x+23)=45$, so $x=11$. Thus, Cathy will be $11+23=34$ years old $3$ years later. 
When Lucy was born, Cathy was $23$ years old. The sum of their ages $3$ years later will be $45$. How old will be Cathy $3$ years later? 
a) $$11$$ 
b) $$15$$ 
c) $$28$$ 
d) $$33$$ 
e) $$34$$ 