On the first day of my holiday, I was at the store and bought a new sombrero for myself, spending half of the money that I had. When I left, I noticed that I had as many cents as I had dollars when I went in, and had half as many dollars as I had cents when I went in.

How much (in dollars) did the sombrero cost?

Note: I had at most 100 coins to start with.

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