To determine the greatest number of name tag stations that Terrell can set up, we need to find the largest number that divides both the 15 name tags and 10 pens evenly, leaving no remainder. This is equivalent to finding the greatest common divisor (GCD) of 15 and 10.

First, let's find the factors of each number:

• The factors of 15 are: 1, 3, 5, 15.
• The factors of 10 are: 1, 2, 5, 10.

The common factors of 15 and 10 are 1 and 5. The greatest common divisor (GCD) is 5.

Therefore, the greatest number of name tag stations Terrell can set up is 5.

This means:

• Each station will receive $\frac{15}{5} = 3$ name tags.
• Each station will receive $\frac{10}{5} = 2$ pens.

Would you like any further details or have any questions? Here are five related questions to expand on this topic:

1. How would the solution change if Terrell had a different number of name tags and pens?
2. What is the process to find the greatest common divisor of two numbers?
3. If Terrell had 20 name tags and 25 pens, what would be the greatest number of stations he could set up?
4. Can you explain why the greatest common divisor is useful in problems like this?
5. How would you solve this problem if you were to consider only one type of item, either name tags or pens?

Tip: Knowing how to find the greatest common divisor (GCD) is useful in many real-life situations involving equal distribution of items.