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?

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.