In the 70s, could a 15 year old...
Open a water-bed store? And a pinball arcade?
And seduce 25 year old women?
SPOILERS
yes...yes...and maybe.
Who is to say that Gary actually seduces Alana...in a sexual manner?
Teenage love can be quite chaste. Certainly in religious couples who "wait for marriage." But with other kids too. The kids can be in love, but for any variety of reasons...sex can wait. One beef I have with attacks on Licorice Pizza is the idea that it is about a SEXUAL relationship. Its not. Its about infatuation, and flirting, and "dating"(going out to dinner)...and a business partnership(Gary is an entrepreneur, Alana wants to do something with her life.) Alana keeps trying to find some sort of connection with OTHER men (the young actor Lance, the old actor Holden, the politician), but they fail her and she always comes back to Gary.
So Gary doesn't seduce Alana...he makes her fall in love with him. And he gets his kiss...earned and finally, at the very end of the movie. Alana's VOICE demonstrates her true love. Listen to this trained singer's articulation of but one word ("Hi") and one sentence ("I love you, Gary") at the end. Sex has noting to do with it. Yet.
Gary may be 15 when the movie starts, but he's probably 16 when it ends. (He can drive.) Two years to "adulthood." In California, maybe, but other US states have lower ages of consent...17...16.
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As to the two businesses. It was the 70's, with less complex tax, business and legal issues. I figure that details were left out. Gary's mother could sign legal documents as an adult. Perahps with the waterbed business, Gary was PARTNERED with the older man(played by Leo DiCaprio's father) whom Gary first met selling water beds.
CONT
Gary has a PR firm (however small) and has been an actor. He has contacts. I'm sure he could put those two businesses together.
And that's another reason that Alana comes to love him. Whatever their REAL ages are, HE's actually about 25 (as a businessman with acting life experience) and SHE's really about 16 (still living at home with her sisters and parents, still under her father's thumb.)
Licorice Pizza is a very precise in the story it wants to tell, but at heart it truly is a very innocent love story. We WANT this couple to get together. We don't get many of those these days.