A square-based pyramid-shaped tent has a base side length of 12 ft and a lateral surface area of 240 sq. ft. Find its slant height and volume, and determine how many tourists can be accommodated if ea

$$240 = 24l$$ $$l = \frac{240}{24}$$ $$l = 10 \text{ ft}$$

The slant height of the tent is $\boxed{\text{10 ft}}$.

We know $l = 10$ ft and $a = 12$ ft.
Using the Pythagorean theorem:

$$l^2 = h^2 + \left(\frac{a}{2}\right)^2$$ $$10^2 = h^2 + \left(\frac{12}{2}\right)^2$$ $$100 = h^2 + 6^2$$ $$100 = h^2 + 36$$ $$h^2 = 100 - 36$$ $$h^2 = 64$$ $$h = \sqrt{64}$$ $$h = 8 \text{ ft}$$

The formula for the volume of a pyramid is:

$$V = \frac{1}{3} \times \text{Base Area} \times h$$

The base is a square with side length $a = 12$ ft, so Base Area $= a^2 = 12^2 = 144$ sq. ft.

$$V = \frac{1}{3} \times 144 \text{ ft}^2 \times 8 \text{ ft}$$ $$V = 48 \times 8 \text{ ft}^3$$ $$V = 384 \text{ ft}^3$$

Each tourist requires 64 cu. ft. of air.

$$\text{Number of tourists} = \frac{\text{Total Volume}}{\text{Air required per tourist}}$$ $$\text{Number of tourists} = \frac{384 \text{ ft}^3}{64 \text{ ft}^3/\text{tourist}}$$ $$\text{Number of tourists} = 6$$

The tent can accommodate $\boxed{\text{6 tourists}}$.