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You could use Enumerable#count:

string.chars.count { |char| vowels.has_key?(char) }

You very rarely need to declare a variable (i in this case), and then modify it form inside a block; there's almost always a better way in Ruby.

So while calling count and passing a block is the most direct, you could also have done something like:

string.chars.select { |char| vowels.has_key?(char) }.count

Same idea, just written out in separate filter/count steps.

You can also skip the return since that's implied at the end of a method.

I'd also use a plain array for the vowels. Looking up hash keys is faster, sure, but does it really matter that much? Nah. "Premature optimization is the root of all evil" and all that.

vowels = %w(a e i o u) # same as ["a", "e", "i", ...]

and then the block becomes:

vowels.include?(char)

If you keep the vowels array sorted, you can use bsearch if you want to speed it up a little. Or you can construct the hash in code, instead of typing all that => 0:

list = %w(a e i o u)
vowels = Hash[list.zip(list)] # => { "a" => "a", "e" => "e", ... }

Of course you could also do something funky like this: Remove all the vowels and see how much shorter the string is afterward:

def count_vowels(string)
  string.length - string.gsub(/[aeiou]/, '').length
end

This is also easily made case-insensitive:

string.length - string.gsub(/[aeiou]/i, '').length

Alternatively, you could extend/monkey-patch the String class a little. I wouldn't recommend it for production code, though. This is just illustrate some Ruby features:

class String
  def vowel?
    self =~ /\A[aeiou]\z/ ? true : false
  end
end

def count_vowels(string)
  string.chars.count(&:vowel?)
end

The &x syntax is a shorthand meaning "invoke x on each element in the collection", so it's equivalent to { |e| e.x }.

Again, this is mostly for fun. I just thought it made the count_vowels method nice and short. And of course, count_vowels could itself be monkey-patched onto String, so you could just call some_string.count_vowels. But again, monkey-patching - while fun - shouldn't be the first thing you reach for. Just illustrating the principle.