To represent the number of packages of cookies that were sold for the fundraiser, let's break down the information provided:

1. Estimated number of cookies sold: 204 cookies.
2. Cookies per package: 12 cookies per package.
3. Estimated number of packages sold: $\frac{204}{12}$.

Next, it was confirmed that $p$ fewer packages were sold than estimated. Therefore, the actual number of packages sold can be expressed as:

$\frac{204}{12} - p$

Simplifying $\frac{204}{12}$ gives:

$17 - p$

So, the expression representing the number of packages of cookies that were sold for the fundraiser is:

$17 - p$

Would you like further details or have any other questions? Here are some related questions:

1. How many packages were sold if $p = 3$?
2. What is the total number of cookies sold if $p = 2$?
3. How would the expression change if the packages contained 10 cookies each?
4. What if the estimated number of cookies was different, say 240? How would that affect the expression?
5. How can you find the total cookies sold if $p$ is known?
6. What happens if $p$ is greater than 17?
7. How would the expression change if instead of $p$ fewer, it was $p$ more packages sold?
8. Can this expression be applied if the number of cookies per package changes?

Tip: Simplifying fractions or expressions early on can make the problem easier to solve and interpret.