Koch traded Machine $1$ for Machine $2$ when the fair market value of both machines was $\backslash$$$50,000.$ Koch originally purchased Machine $1$ for $\backslash$$$75,000,$ and Machine $1\text{'}$s adjusted basis was $\backslash$$$40,000$ at the time of the exchange. Machine $2\text{'}$s seller purchased it for $\backslash$$$65,000$ and Machine $2\text{'}$s adjusted basis was $\backslash (\backslash$$ $55,000\backslash )$ at the time of the exchange. What is Koch's adjusted basis in Machine $2$ after the exchange?

Multiple Choice

$\backslash$$$40,000$

$\backslash$$$50,000$

$\backslash$$$55,000$

$\backslash$$$75,000$

None of the choices are correct.