https://file.aiquickdraw.com/mathbot/file/1727323559957wwcsvpvg.jpg

Let's break down the problem from the image you've uploaded.

We are told that:
- Six Grade 2 learners sit around one table.
- When two tables are joined, eight learners sit around them.

We need to calculate how many learners would sit at different numbers of tables: five tables, twenty-five tables, and two hundred tables.

### Step-by-step breakdown:
1. **For one table**: 6 learners sit around one table.
2. **For two tables**: 8 learners sit around the two joined tables.

From this, we can deduce that by joining an additional table to an existing setup, 2 more learners are added.

This suggests a pattern where after the first table, each additional table adds 2 more learners.

### Formula Derivation:
- For \( n \) tables: The number of learners is 6 learners (for the first table) plus 2 learners for each additional table.
- General formula:
\[
\text{Learners} = 6 + 2 \times (\text{number of tables} - 1)
\]

### Now we apply this formula to the given scenarios:

#### 2.4.1 Five tables:
\[
\text{Learners} = 6 + 2 \times (5 - 1) = 6 + 2 \times 4 = 6 + 8 = 14
\]
So, 14 learners would sit at five tables.

#### 2.4.2 Twenty-five tables:
\[
\text{Learners} = 6 + 2 \times (25 - 1) = 6 + 2 \times 24 = 6 + 48 = 54
\]
So, 54 learners would sit at twenty-five tables.

#### 2.4.3 Two hundred tables:
\[
\text{Learners} = 6 + 2 \times (200 - 1) = 6 + 2 \times 199 = 6 + 398 = 404
\]
So, 404 learners would sit at two hundred tables.

### Summary:
- For 5 tables: 14 learners.
- For 25 tables: 54 learners.
- For 200 tables: 404 learners.

Would you like further clarification or additional details?

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**Relative Questions:**
1. What would be the number of learners for 10 tables?
2. How many learners would sit at 50 tables?
3. What if we used 3 tables instead of 2 for the same calculation pattern?
4. How many learners would sit if each new table added 3 learners instead of 2?
5. Can this pattern apply if the tables form a different geometric arrangement?

**Tip:** Always check if there is a pattern in the changes (increase or decrease) between cases when calculating a series of related values. This helps in formulating general rules.

Six Grade 2 learners sit around one table; the teacher joins the two tables, and eight sit on the two tables. Calculate how many learners would sit at the following tables: five tables, twenty-five tables, and two hundred tables.

Learn how to calculate the number of learners sitting around a set of tables, starting with 6 learners at one table, following an arithmetic pattern where 2 additional learners are added for each additional table. The solution includes step-by-step calculations for 5, 25, and 200 tables.

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