Math CentralQuandaries & Queries


Question from Lydia:

The sum of the ages of Ruth and her mother is 77 years. The difference in their ages is 27 years. How old is each?

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.


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