Jane is seven years older than amy. twelve years ago, amy was half as old
as jamie is now. how old is jamie now?

Jane+7=amy's age
7x2=14  14/2=7
j14=a7
amy -    7 +12years =19years now

J=jane's age now
a=amy's age now
a-12=amy's age 12 years ago

j is 7 older than a
j=7+a

12 years ago
amy was 1/2 as old as jamie is now
a-12=(1/2)j

so
j=7+a
sub 7+a for j

a-12=(1/2)(7+a)
times 2 both sides
2a-24=7+a
minus a both sides
a-24=7
add 24 both sides
a=31

j=7+a
j=7+31
j=38

jamie is 38 now