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Ezra and Zoe are playing the new video game Knights of the Dawn. At the start of level $7$, Ezra had two-thirds as many gold coins as Zoe. During the level, Ezra found $32$ gold coins, but Zoe only found $6$. At the end of the level, both players had the same number of gold coins.$\newline$Which equation can you use to find $z$, the number of gold coins Zoe had at the start of level $7$?$\newline$Choices:$\newline$(A) $z = \frac{2}{3}z + 32 + 6$$\newline$(B) $\frac{2}{3}z + 32 = z + 6$$\newline$How many gold coins did Zoe have at the start of level $7$?$\newline$____ gold coins$\newline$