Rather late for the original question, but I think there are 30 keys in Western music.
7 flats through zero then 7 sharps, major and relative minor.

It can be argued there are many more, though, as the fifteen time-signatures each have seven modes, giving 105. And Blues and mixo-blues and... There undoubtedly more, because much music from other cultures doesn't fit neatly our Western 12-note scale.

Enough sums already. :-)

Jazz relative beginner, starting at a much older age than was helpful.
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