Baby Houseman was 17 years old

How old is Baby Houseman in the movie Dirty Dancing?

The answer is mentioned in article by Carrie Nelson, titled An Interview with Eleanor Bergstein: On Dirty Dancing, Feminism and the Film Industry, published in 2010 by the website Gender Across Borders.

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On whether or not Dirty Dancing is autobiographical:
.... I was called “Baby” ‘til I was 22, I went to the Catskills with my parents, I was dirty dancing from the time I was 10. I got dirty dancing trophies that would turn your hands green if you touched them.

There’s not a second in it that isn’t in some way part of my life and my history, but I’m in all the characters, as most writers are. Everything about it I hope is truthful, and a great deal of it came from particular elements of my life. But, you know, that’s different from saying I sat down to write my 17th summer.

On Dirty Dancing’s political backdrop:
I wanted to use that world, which was my parent’s world – what I would call “The Last Summer of Liberalism” – when the world had one foot in either camp, but it was about to change, as Max says at the end.

The following summer, the summer of ’64, you couldn’t have told that story, because all that music was above ground then, and all the guests would have been doing that kind of rock band thing, so perhaps not as erotic as the dirty dancing ... This was the last summer there could be an upstairs and a downstairs in that way.

I’m always very anxious to be in those moments just before transition. I was enormously interested in bringing back that time, both politically and socially in America, when everybody really believed that the world had been made safe by World War II, and the only thing left to do was to make it safe for everybody. So, the large Jewish community gave lots and lots of money to SNCC and CORE and supported the Freedom Riders. ...

On Dirty Dancing’s abortion subplot:
What I wanted was to have something like that in a mainstream movie, even though we didn’t think many people would see it. If you do a documentary on coat-hanger abortions, the only people who see it will be those who agree with you anyway. If you put one in a wide-based musical with pretty clothes, and lots of romance, it may surprise people and make them think of things they didn’t think of before. ...

I always thought if you were going to put any kind of message in, it has to be as carefully plotted in as that,
because if it’s at all adjacent, it’s going to end up on the cutting room floor. So that was fine. Not many people talked about it, except that we got a very, very big feminist audience.

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In the article, Bergstein remarks also on the following two subjects:

On the state of women in the film industry today

and

On discovering the feminist blogosphere