suggest XLR balanced to RCA hardware?

I'm running two soundsystems in my apartment from a DJ mixer. One system is currently running via a really long RCA cord to the other room. I would like to utilize the XLR out on my mixer, but my integrated amp is RCA in only. I was wondering if someone could recommend a piece of hardware that would be appropriate for keeping a balanced signal over a long distance (so balanced XLR ins) with an RCA output (a short cable to go to my integrated amp). Right now I don't even know what such a device is called. I'm looking for a solid piece of equipment, but nothing too expensive (<$150 if possible).
Hi Brandle

Since you are familiar with pro audio gear how about this solution?

Rane BB 44X Balance Buddy.

Used it can go for about $160 or less. It does XLR to RCA and vice versa.

If not what about Hosa or Switchcraft XLR to RCA adapters?
Thanks, I really like the Rane mixers I've had, so I might give the balance buddy a try.
Regarding adapters, I was under the impression that, in order for the signal to stay balanced, it would have to go into another piece of hardware with balanced inputs. Using an XLR to RCA adapter wouldn't keep the signal balanced. Is that correct?
Here’s an inexpensive Balanced to Unbalanced line converter that will go in both directions .. you can input XLR and output RCA or input RCA and output XLR

It also has input and output volume controls for fine tuning

Run your DJ mixer via long XLR cable to the other room and put Converter right next to the intergrated amp system and hook up via the RCA output of the converter with a short single ended RCA cable

I use one to go from unbalanced RCA OUT to XLR balanced IN on my external cross over for my Subs .. you would use in the other direction XLR out from mixer to RCA in on the intergrated amp system

At $39 plus shipping .. don’t let the price fool you .. look at the specs 90db signal to noise and 0.003 THD .. I’m sure this wouldn’t degrade your mixer to other room system

Balanced to Unbalanced line converter ... CLICK HERE