The first week you ate 2 spoons of nuts every day, for a total of 14 spoons of nuts.
For the next [tex]w[/tex] weeks (i.e. the next [tex]7w[/tex] days) you ate 3 spoons per day, for a total of [tex]21w[/tex] spoons of nuts.
In total, you ate [tex]14+21w[/tex] spoons of nuts in [tex]7+7w[/tex] days, for an average of
[tex]\dfrac{14+21w}{7+7w}=\dfrac{2+3w}{1+w}[/tex] spoons per day.
If each spoon has 3 nuts, in the first week you ate 2 spoons per day, i.e. 6 nuts per day. In the next weeks you ate 3 spoons per day, i.e. 9 nuts per day.
