The present age of a father is equal to sum of ages of his son and daughter. Ten years ago from now, the age of the father was double the age of the son and four times the age of the daughter. The total present age of the father, daughter and son is ____ years.
100
Let the present ages of son and daughter be S and D, so father's age \(F=S+D\).
Ten years ago: \(F-10=2(S-10)\) and \(F-10=4(D-10)\).
From the first: \(F=2S-10\). Combined with \(F=S+D\): \(S+D=2S-10 \Rightarrow D=S-10\).
From the second: \(F=4D-30\). Substituting \(F=S+D=2D+10\): \(2D+10=4D-30 \Rightarrow D=20,\ S=30,\ F=50\).
Total present age: \(F+S+D = 50+30+20 = 100\).
Hence, the total present age of the father, daughter and son is 100 years.
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