The sum of the ages of a daughter and her mother is 76 years. After 4 years, the age of the mother will be three times that of the daughter. What is the present age (in years) of the mother?
59
Let the present ages be daughter \(d\) and mother \(m\), with \(d + m = 76\).
After 4 years the ages become \(d + 4\) and \(m + 4\), and the mother is three times the daughter: \(m + 4 = 3(d + 4)\).
From the sum, \(m = 76 - d\). Substitute: \(76 - d + 4 = 3d + 12\).
Simplify: \(80 - d = 3d + 12\), so \(68 = 4d\) and \(d = 17\).
Then the mother's present age is \(m = 76 - 17 = 59\).
Hence, the present age of the mother is 59 years.
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