You only need one of the smaller kids quad bike as long as it has the front brakes and they are often pretty cheap
Norm the small 50 cc 2 stroke front disc brake kids quad bike will not be suitable as it's recommended loading weight is 50 kg
and I don't think those small disc brakes would do much for a heavy ride on mower.
I guess it you go to the trouble of getting a quad bike you may as well buy a $100. 110 cc to 125cc 4 stroke quad bike and just
make the tow mower.
Cheers
Max.
