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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? 
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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. 