To solve this problem, let's analyze the data provided to find the length added by each nested cart.

Problem Analysis:

Each row has a starting cart that is 4 feet long. Then, additional nested carts increase the total length of the row.

Given points:

• A row with 0 nested carts is 4 feet.
• A row with 13 nested carts is 23.5 feet.
• A row with 18 nested carts is 31 feet.

We need to find the amount of length each nested cart adds.

Solution Approach:

1. Let's denote:

   • $L$ as the total length of the row.
   • $n$ as the number of nested carts.
   • $m$ as the additional length each nested cart adds.

2. We can use the formula: $L = 4 + m \times n$ where 4 feet is the starting length of the row without any nested carts.

3. Let's use the two points to set up equations:

   • For $n = 13$: $L = 23.5$ $23.5 = 4 + 13m$
   • For $n = 18$: $L = 31$ $31 = 4 + 18m$

4. Solving these equations:

   • From the first equation: $23.5 - 4 = 13m \Rightarrow 19.5 = 13m \Rightarrow m = \frac{19.5}{13} = 1.5$

   • Therefore, each nested cart adds 1.5 feet to the length of the row.

Answer:

Each nested cart adds 1.5 feet to the length of the row.

Would you like a detailed breakdown of the solution, or have any further questions?

Here are five additional related questions:

1. How would the length of a row with 10 nested carts be calculated?
2. Can you derive the general formula for the row length if you know the number of nested carts?
3. What would be the total row length with 20 nested carts?
4. How could this model change if the starting cart had a different length?
5. How would the length change if each nested cart added 2 feet instead?

Tip: Remember to always check if your linear equation fits all given data points.