Rei is barricading a door to stop a horde of zombies. She stacks boxes of books on a table in front of the door. Each box weighs 
 
 kilograms, and the table with 
 
 boxes on top weighs a total of 
 
 kilograms.
The total weight 
 
 of the barricade in kilograms is a function of 
 
, the number of boxes Rei stacks on the table.
Write the function's formula.

Let's denote the following:
- \( w \) as the weight of each box in kilograms,
- \( n \) as the number of boxes,
- \( W \) as the total weight of the table with \( n \) boxes on top.

Given that the total weight \( W \) is a function of the number of boxes \( n \), we need to find the formula for this function.

The total weight \( W \) includes:
1. The weight of the table itself, which we will denote as \( T \) kilograms.
2. The weight of \( n \) boxes, where each box weighs \( w \) kilograms.

Therefore, the total weight \( W \) can be expressed as:
\[ W = T + nw \]

In this formula:
- \( T \) is the constant weight of the table.
- \( nw \) is the combined weight of \( n \) boxes, where each box weighs \( w \) kilograms.

So the function \( W(n) \) representing the total weight of the barricade in kilograms as a function of the number of boxes \( n \) is:
\[ W(n) = T + nw \]

Would you like any more details or have any questions?

Here are 5 questions you might ask next:
1. How can we determine the value of \( T \) if we know the total weight for a specific number of boxes?
2. What happens to the function if the weight of each box changes?
3. Can we graph this function \( W(n) \)?
4. How would we solve for \( n \) if we know the total weight \( W \) and the weights of the table and the boxes?
5. How can this function be used to optimize the number of boxes for a given maximum weight capacity?

**Tip:** When working with linear functions, understanding how each variable and constant affects the equation helps in visualizing and solving real-world problems effectively.

Learn how to calculate the total weight of a barricade using linear functions. Understand the formula W(n) = T + nw, where W(n) represents the total weight, T is the weight of the table, n is the number of boxes, and w is the weight of each box. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation