A swimming pool 10 m long and 8 m wide is surrounded by a path of uniform width. If the area of the path is 88 m², find the width of the path.

The dimensions of the swimming pool are 10 m long and 8 m wide.
The dimensions of the pool including the path will be:
Length $= (10 + 2x)$ m
Width $= (8 + 2x)$ m

The total area is given as 168 m$^2$.

We can factorize the quadratic equation. We need two numbers that multiply to $-22$ and add up to 9. These numbers are 11 and $-2$.

This gives two possible solutions for $x$:

Since the width of a path cannot be negative, we take the positive value.

The width of the path is $\boxed{2 \text{ m}}$.

Area of the pool $= 10 \text{ m} \times 8 \text{ m} = 80 \text{ m}^2$.
Total area of pool and path $= 168 \text{ m}^2$.
Area of the path $= \text{Total area} - \text{Area of pool}$

The side of each corner slab is equal to the width of the path, which is 2 m.
Area of one corner slab $= 2 \text{ m} \times 2 \text{ m} = 4 \text{ m}^2$.
There are 4 corners, so 4 corner slabs.
Area covered by corner slabs $= 4 \times 4 \text{ m}^2 = 16 \text{ m}^2$.

Area covered by smaller slabs $= \text{Area of path} - \text{Area covered by corner slabs}$

The side of each smaller slab is 50 cm, which is 0.5 m.
Area of one smaller slab $= 0.5 \text{ m} \times 0.5 \text{ m} = 0.25 \text{ m}^2$.
Number of smaller slabs $= \frac{\text{Area covered by smaller slabs}}{\text{Area of one smaller slab}}$

The number of smaller slabs used is $\boxed{288}$.

Number of corner slabs $= 4$.
Cost of each corner slab $= \text{sh } 600$.
Cost of corner slabs $= 4 \times 600 = \text{sh } 2400$.

Number of smaller slabs $= 288$ (from part b(i)).
Cost of each smaller slab $= \text{sh } 50$.
Cost of smaller slabs $= 288 \times 50 = \text{sh } 14400$.

Total cost $= \text{Cost of corner slabs} + \text{Cost of smaller slabs}$

The total cost of the slabs used to cover the whole path is $\boxed{\text{sh } 16800}$.