A girl is now one-fourth as old as her father, and in seven years, she will be one-half as old as her father was twelve years ago. What are her and her father's present ages?

father's age = 20; daughter's age = 5
father's age = 52; daughter's age = 13
father's age = 76; daughter's age = 19

Question

A girl is now one-fourth as old as her father, and in seven years, she will be one-half as old as her father was twelve years ago. What are her and her father's present ages?

father's age = 20; daughter's age = 5
father's age = 52; daughter's age = 13
father's age = 76; daughter's age = 19

anonymous · Answer

so, if f is the father's age, and d the daughter's,
d=f/4
and
d+7=(f-12)/2
then by substituting f/4 into the second equation,
f/4+7=f/2-6
f/4=13
f=52
and we're done!