Let:

• $x$ be the number of small boxes purchased.
• $y$ be the number of large boxes purchased.

We are given the following information:

1. Each small box contains 50 nails.
2. Each large box contains 350 nails.
3. The contractor bought 3 more small boxes than large boxes, so $x = y + 3$.
4. The total number of nails is 2950.

Now, let's write the system of equations:

1. The first equation comes from the relationship between the number of small and large boxes: $x = y + 3$

2. The second equation comes from the total number of nails: $50x + 350y = 2950$

So, the system of equations is: $x = y + 3$ $50x + 350y = 2950$

This system can be solved to find the number of small boxes $x$ and large boxes $y$.

Would you like me to solve this system for you?

Here are 5 related questions:

1. How would you solve this system of equations by substitution?
2. Can you express the total number of nails in terms of only one variable?
3. What would happen if the number of nails per box changed?
4. How many large boxes were bought if the contractor bought 5 small boxes?
5. Could this system be solved graphically? How would that look?

Tip: Always double-check the relationships and units when setting up systems of equations based on word problems!