A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 50 nails and each large box has 350 nails. The contractor bought 3 more small boxes than large boxes, which altogether had 2950 nails. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
Answer
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Let
equals=
the number of small boxes purchased
.
Let
equals=
the number of large boxes purchased
.
System of Equations:

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!

A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 50 nails and each large box has 350 nails. The contractor bought 3 more small boxes than large boxes, which altogether had 2950 nails. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.

Learn how to set up and solve a system of equations to determine the number of small and large boxes purchased by a contractor. This problem explores algebraic methods, including substitution, to solve for unknowns. Suitable for students in Grades 8-10.

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