The sum of ages of a mother and daughter is $45$ years. Five years ago, the product of their ages was four times the mother's age at that time. The present age of the mother is?

Let the mother's present age be M and the daughter's be D, so M plus D equals 45. Five years ago, the product of their ages was (M minus 5) times (D minus 5), which equals 4 times (M minus 5). This simplifies to D minus 5 equals 4, meaning D is 9. Substituting D into the first equation gives M plus 9 equals 45, so M equals 36. The mother is 36 years old.

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