How can I play music from a mac mini in another room on a stereo system

1 drag a long minijack to RCA cable to the stereo and connect that to some RCA input (not vinyl if it has that because it apm too much)

pro: cheap, cable looks like this http://multiroomaudioplayer.com/wp-content/uploads/2015/08/rca_minijack.jpg

con: trip over the wire, long cables works as antennas mess up the sound quality

2 get a Bluetooth to minijack dongle Bluetooth Aux Adapter | eBay and use a short mini to RCA if the stereo does not have minijack input

pro: not too pricy will also work with other devices then your macmini such as other computers and tablets and smart phones

con: cheaper ones can give issues

3 get an airport express and use airplay to choose what speakers you wish to play out of

pro: let you output to more then 1 audio source, works well in the apple setup

con: apple discontinued it so it will not get the new airplay2 features and the most expensive of the options

It would help if we knew a bit more about your stereo system. For example does it support analog or optical digital audio inputs? If so, one method to stream music from your Mac mini is to use an AirPort Express base station. This base station can be configured to join an existing Wi-Fi network. In turn, you would connect the appropriate audio cable between the Express and your stereo's audio input port. You would then, for example, stream audio from iTunes, via AirPlay, to the Express and have it output via your stereo system.

I use Airplay from iTunes to my Yamaha receiver which has the Airplay feature. Works great.