$($b$)$ The town of Thohoyandou maintains a constant population of $400000$ people from year to year. A political science study estimated that there were $150000$ EFF, $90000$ANC and $60000DA$ members in the town. It was also estimated that $20$ percent of the EFF join ANC and $10$ percent join DA each year. Similarly, $20$ percent of ANC members become EFF members and $10$ percent join the DA$,$ while $10$ percent of the DA members defect to the ANC and $10$ percent become EFF each year.