



 
Hi Lydia, I think you are expected to use algebra to solve this problem so I am going to say that Ruth's age is $R$ years and her mother's age is $M$ years. Since the sum of their ages is 77 years \[M + R = 77.\] You also know that the difference in their ages is 27 years so \[M  R = 27.\] Solve the pair of equations. Make sure that you verify your answer. Penny 



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