This may sound silly. But I'm really confused why, when we pronounce (the phoneme) /k/, we sometimes spell it with a C and sometimes with a K (sometimes with CK).
Why wasn't 'k' used instead, in such words as: car, cake, etc...?

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    Because our writing system is largely derived from the Roman alphabet, which didn't originally have a K; it got that letter from Greek (which, in turn, didn't really have a C). – Matt Gutting Apr 8 '15 at 16:44
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    I think the whole question of why orthography and spoken usage are (or become) so out of step is Too Broad. But on this specific point I think it makes more sense to ask why the sound /k/ is sometimes written using the letter c, rather than why that letter is sometimes pronounced that way. – FumbleFingers Apr 8 '15 at 16:51
  • c is generally pronounced like k when followed by vowels a, o, or u, it's pronounced like s when followed by e, i, or y. – Barmar Apr 8 '15 at 16:56
  • English has a number of letters that are pronounced differently depending on their context. This is most common with vowels, which have long and short forms (and variations within them), but there are also some consonants that vary. – Barmar Apr 8 '15 at 16:58
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    You're working from the wrong concept. Letters don't make sounds; sounds are represented in letters. So what you mean is why, when we say /k/, we sometimes spell it with a C and sometimes with a K (and of course sometimes with CK, for good measure). And the answer is that we are in the habit of spelling words in certain ways, because of how they were spelled and sometimes because of how they were pronounced in a different language, at the time and place they were borrowed into English. And not from how they're pronounced now in modern English. It's 400-year-old software, for Pete's sake. – John Lawler Apr 8 '15 at 17:40