9 years ago Jane was twice as old as Millie. The sum of their ages now is 35. How old is Millie now?

Let's translate the word problem into a system of equations. Let #J# be Jane and #M# be Millie.

Jane was twice as old as Millie #9# years ago. That means we will have to double #m# and subtract #9# from J.

#J-9=2M#

Adding their ages together will give #35#

#M+J=35#

Our problem is in an easy situation for substitution. However, you could use elimination if you wanted to. I will stick with substitution. Solve for #J# in the first equation:

#J=2M+9#

Now plug it into the other equation:

#M+2M+9=35#

Consolidate #M#s:

#3M+9=35#

Subtract #9# on both sides:

#3M+9-9=35-9#

This becomes:

#3M=26#

Divide both sides by #3#:

#(3M)/3=26/3#

This becomes:

#M=26/3#

Now we can plug this back into one of the original equations. I will plug it into the second equation:

#26/3+J=35#

Subtract both sides by #26/3#:

#26/3+J-26/3=35-26/3#

This becomes:

#J=79/3#

So Millie is not #13# and Jane is not #22#

We are working with two people and 2 periods of time.
Jane and Millie were both #9# years younger than their present age.

Millie is the younger of the two, let her present age be #x# years.

#color(white)(wwwwww#9 years ago#color(white)(wwww)#present age

Millie:#" "x-9" "larr color(white)(wwwww)color(red)(x)"#
#color(white)(..................)darr#
Jane:#" "color(blue)(2(x-9))" "rarr" "color(red)(2(x-9)+9)#

#9# years ago Jane was twice as old as Millie. (#color(blue)(2(x-9))#)

Jane's present age is #9# years older than #9# years ago.

The #color(red)("sum of their present ages is "35)#

#color(red)(x+2(x-9)+9 =35)#

#x+2x-18+9 =35#

#3x-9 =35#

#3x = 44#

#x = 44/3 = 14 2/3" "larr# Millie's present age

#35- 14 2/3 = 20 1/3" "larr# Jane's present age

Millie is 14 years and 8 months old and
Jane is 20 years and 4 months old.