'answer a need' is correct and usable in written English.
You can use it when you want to describe something that fulfills a requirement or solves a problem. For example: "This new business venture promises to answer a need in the community for affordable healthcare services."
Customs exist because they answer a need; when they disappear, that need must be met in some other way.
What alarms China's leaders now about the seemingly sudden emergence of the Falun Gong sect is that it may answer a need no longer answered by the party.
A Clarence House spokesman said: "By creating the Education Summer Schools… he was helping to answer a need, which was expressed by head teachers and heads of departments in schools across England".
It would be fairer to say that, like much else that is very old, it is on occasion taken out of the closet, dusted off, and put on display to answer a need.
Something very similar might be said about self-help books, which seem to answer a need ("I don't understand my husband"), but which really just create a new need ("I need to read this book because it makes me feel I've understood my husband").
FOREIGN imports, including Patrick Marber's "Closer," Steven Berkoff's "East" and Paula Vogel's "How I Learned to Drive," answer a need among the new wave of private theater companies to sell tickets to a young audience with a new Hollywood-inspired taste for sex, violence and obscene language.
"The distributor answers a need for daydream moments in an extremely organized urban space," Langlois said.
This approach partially answers a need expressed by Wilson to develop useful consilience methodology, including maps and other orientation devises.
Verdi answers a need for emotional realism that pop music once offered in abundance but is now failing to provide.
The trade answered a need for the defending Stanley Cup champions, who were in search of defense.
