The total kg of rice bought is 75kg
Each week, 4.5kg is used,
Let the number of weeks be represented by n
The remaining amount of rice is represented by r
The relationship between the values above can be given as,
[tex]r=75-4.5n[/tex]For 6 weeks, the kilogram of rice left where n = 6 is,
[tex]\begin{gathered} r=75-4.5n \\ r=75-4.5(6)=75-27=48\operatorname{kg} \end{gathered}[/tex]For 12 weeks, the kilogram of rice left where n = 12 is,
[tex]\begin{gathered} r=75-4.5n \\ r=75-4.5(12)=75-54=21\operatorname{kg} \end{gathered}[/tex]For w weeks, the kilogram of rice left where n = w is,
[tex]\begin{gathered} r=75-4.5n \\ r=75-4.5(w)=75-4.5w \end{gathered}[/tex]Hence, after 6 weeks, the remaining rice left is 48kg
Hence, after 12 weeks, the remaining rice left is 21kg
Hence, after w weeks, the remaining rice left is (75-4.5w)kg