Neco 2018 Civic Education Question 15

Over a five‑year period a peace‑building agency wants to reduce the number of communal conflicts in a state from \(120\) incidents per year to no more than \(30\) incidents per year. The agency can run two types of programmes:\n\n- Mediation workshops: each (if successfully completed) reduces the annual incident count by \(5\). Success rate = \(80\%\).\n- Community dialogue sessions: each (if successfully completed) reduces the incident count by \(3\). Success rate = \(90\).\n\nThe agency can plan a total of \(30\) programmes (workshops plus sessions) over the five years. Let \(x\) be the number of workshops and \(30-x\) the number of dialogue sessions. Assuming only the successful programmes produce reductions, what is the minimum integer value of \(x\) required to achieve the target (i.e., bring incidents down to \(\le 30\) per year)?