A shipping company needs to transport cargo containers from one port to another. Each container has a weight limit of 20 tons, and the ship's maximum capacity is 500 tons. The company charges $200 per ton for transportation. However, if a customer ships more than 10 containers, they receive a 10% discount on the total cost. Calculate the number of containers that can be shipped, the total cost for a customer shipping 15 containers, and explain your reasoning.

First, we need to determine the maximum number of containers that can be shipped based on the ship's capacity. To do this, divide the ship's maximum capacity by the weight limit per container:

500 tons / 20 tons/container = 25 containers

So, the shipping company can transport up to 25 containers at a time.

Next, let's calculate the total cost for a customer shipping 15 containers. First, find the total weight of these containers:

15 containers * 20 tons/container = 300 tons

Now, multiply the total weight by the cost per ton:

300 tons * $200/ton = $60,000

Since the customer is shipping more than 10 containers, they receive a 10% discount on the total cost. Calculate the discount amount:

$60,000 * 0.1 = $6,000

Subtract the discount from the original cost to find the final cost:

$60,000 - $6,000 = $54,000

Therefore, the shipping company can transport up to 25 containers at a time, and the total cost for a customer shipping 15 containers with a 10% discount would be $54,000.