Mrs. Wilson had three children: Edgar, James, and John. Their combined ages were

Question

Mrs. Wilson had three children: Edgar, James, and John. Their combined ages were half of hers. 5 years later, during which time Ethel was born, Mrs. Wilson's equalled the total of all her children's ages. 10 years more have now passed, Daisy appearing during that interval. At the latter event, Edgar was as old as John and Ethel together. The combined ages of all of the children are now double Mrs. Wilson's age, which is, in fact, only equal to that of Edgar and James together. Edgar's age also equals that of the two daughters. Find all of their ages now.(clue: two of them are twins)

Explanation / Answer

Wow! Lots of information. Start by assigning each person a letter... W for Mrs Wilson, E for Edgar, J for James and H for John (or w, x, y, z or however you'd like to do it). Write as many equations as you can from the information given, but leave the letters alone. As time passes, write the person as their original letter + years. For example, If you write E+J+H = W/2 for the first sentence, you'll use (E+5)+(J+5)+(H+5)+(T+x)=W (where x is between 1 and 5 years for Ethel) Keep writing formulas. When you have them listed out, you can start solving each equation for a specific letter (find an 'easy' one) and substitute it into other equations, simplifying as you go. For example, in the first equation I wrote, I could rewrite it as 2x (E+J+H)=W and then use that to merge with my second equation to get 2x (E+J+H) = (E+5)+(J+5)+(H+5)+(T+x) since we know that they both equal W. Good luck!

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