The monthly admission fee to a public pool is $42. It costs an additional p dollars to rent a locker to hold your belongings. The total cost for 8 people to enter the public pool and each rent a locker is $360. How much does it cost for one person to rent a locker?

Let's assume the cost to rent a locker is p dollars.

So, the total cost for 8 people to rent a locker is 8 * p = 8p dollars.
The total cost for monthly admission fee and renting a locker for 8 people is 8p + 42 = $360.
So, 8p = $360 - $42.
Therefore, 8p = $318.
Hence, the cost for one person to rent a locker is p = $318 / 8 = $<<318/8=39.75>>39.75. Answer: \boxed{39.75}.

Let's set up the equation to solve for the cost of renting a locker.

The monthly admission fee is $42, and it costs an additional p dollars to rent a locker.

So, the cost for one person to enter the public pool is $42 + p.

There are 8 people in total, so the cost for 8 people to enter the pool is 8 * ($42 + p).

The total cost for 8 people to enter the pool and each rent a locker is $360.

Therefore, we can set up the equation:

8 * ($42 + p) = $360

Now let's solve for p.

8 * $42 + 8 * p = $360
336 + 8p = $360
8p = $360 - $336
8p = $24

Dividing both sides by 8, we get:

p = $24 / 8
p = $3

Therefore, it costs $3 for one person to rent a locker.