Problema Solution
Twelve years ago, a man was three times as old as his daughter. Nine years from now, the man will be twice as old as his son. Four years from now, the sum of the ages of the son and the daughter will equal the age of the man. How old is each now?
Answer provided by our tutors
let
m = the age of the man
d = the age of the daughter
s = the age of the son
Twelve years ago, a man was three times as old as his daughter.
m - 12 = 3(d - 12)
m - 12 = 3d - 36
m = 3d - 24
Nine years from now, the man will be twice as old as his son.
m + 9 = 2(s + 9)
m + 9 = 2s + 18
m = 2s + 9
Four years from now, the sum of the ages of the son and the daughter will equal the age of the man
m + 4 = d + 4 + s + 4
m + 4 = d + s + 8
by solving the system of equations
m = 3d - 24
m = 2s + 9
m + 4 = d + s + 8
we find
s = 18 years
d = 23 years
m = 45 years
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the man is 45 years old now.
the daughter is 23 years old now.
the son is 18 years old now.