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(I added some emphasis and changed the wording of the last statement.) What is important is that you have selected one girl, Sarah, and expressed each girl's age as a fraction of Sarah's age. A more conventional algebraic way to write this is to let M, R and S be the three girl's ages and then your statements are
You then expressed the three fractions with the same denominator and added the three equations to get
which you know is 46 so 23/6 S = 46 and hence S = 12. For your second problem you have
Mary's age is common in the two statements, which is why I wrote it on the right, so to make this work I need to express Ruth's age as a fraction of Mary's age. If 9/8 of Ruth's age is Mary's age then 8/9 of Mary's age is Ruth's age. Thus the three statements (equations) become
Expressing each fraction with a denominator of 9 gives a sum of 23/9. If the sum is of the ages is 46 then 23/9 of Mary's age is 46 so Mary's age is 18. Penny  


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