Question

I eat 2 spoons of nuts every day for a week. Then I eat 3 spoons for the following w weeks. How many spoons did I eat on average per day?
IGNORE THAT BUT WHAT DO I DO FOR 2ND PART
Each spoon has 3 nuts. How many nuts do I eat each day?

Answer 1

The first week you ate 2 spoons of nuts every day, for a total of 14 spoons of nuts.

For the next $w$ weeks (i.e. the next $7w$ days) you ate 3 spoons per day, for a total of $21w$ spoons of nuts.

In total, you ate $14+21w$ spoons of nuts in $7+7w$ days, for an average of

$\dfrac{14+21w}{7+7w}=\dfrac{2+3w}{1+w}$ 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.