According to calculations, Lady Capulet says, "By my count, I was your mother much upon this years that you are now a maid". This seems to say that Lady Capulet was thirteen when she had Juliet and since Juliet will be 14 years of age, at the conclusion of the ball, that would make Lady Capulet 27 years old. It was the custom in the day that young ladies were married at the early age of 13 and should feel privileged when a gentleman asked for their hand in marriage.
Source: The Language and Literature Book by McDougal Littell.
It appears that Lady Capulet was quite young when Juliet was born. When she is introducing the idea of marriage to Juliet before the masque in Act I Scene 3, she mentions that she was already a mother by Juliet's age, which is not quite 14:
Well, think of marriage now: younger than you,
Here in Verona, ladies of esteem,
Are made already mothers: by my count
I was your mother much upon these years
That you are now a maid. Thus, then, in brief;--
The valiant Paris seeks you for his love.
Lady Capulet was almost 14 when she had Juliet because in the play , she told Juliet that she was the same age as her when she had her . Since we know that Juliet was turning 14 soon , we can infer that Lady Capulet was almost 14 too .