
Since one table has three sides and each seats one child, it follows that 3 children can sit around 1 table.
When two tables are put together in a row as pictured, then we can count the number of open sides around the perimeter of the two tables together, since an open side means one child can sit there. There are 4 sides that are open around the table, and so 4 children can sit around a row of 2 tables.
Using the same method as above, we see that when 3 tables are put into a row we will have 5 open sides around the tables. So, 5 children can sit around a row of 3 tables.

To find an expression that describes the number of children that can sit around a row of $n$ tables, we can consider the diagram below. We see that we can fit 1 child at each horizontal table side (black dots) plus 1 child on the left and one on the right (white dots). So we have:
$$
\text{children that can sit at } n \text{ tables} = n + 1 + 1 = n + 2
$$
Another way to think about counting seats is shown in the picture below. The first table seats two children and the last table seats two children (white dots). All other $n  2$ tables seat one child (black dots). So we have:
$$
\text{children that can sit at } n \text{ tables} = 2 \cdot 2 + (n  2) \cdot 1 = 4 + (n  2).
$$
Other expressions are also possible, which are all equivalent to $n + 2$.

Using our expression from part (b), with $n=125$, we see that
$$n + 2 = 125 + 2 = 127,$$
so 127 children can sit around a row of 125 tables.
Using our expression from before we know that a row of $n$ tables seats $n + 2$ children. If we want to seat 26 children we need to find n such that $n + 2 = 26$. So we have $n = 24$, which means that the teacher needs 24 tables to seat all students in the class.