Let's break down the problem:

We have three cards, and we are given the following information:

1. The minimum of the set of numbers is 2.
2. The range of the numbers is 9.
3. The mean (average) of the numbers is 7.

Let the three cards have the values: $2$, $x$, and $y$.

Step 1: Using the range

The range is the difference between the largest and the smallest number. Since the minimum number is 2 and the range is 9, we can determine the largest number: $\text{Largest number} = 2 + 9 = 11$ So, one of the other numbers must be 11.

Step 2: Using the mean

The mean (average) of the three numbers is given as 7. The formula for the mean is: $\frac{2 + x + y}{3} = 7$ Multiplying both sides by 3: $2 + x + y = 21$ Since we know one of the numbers is 11, substitute that into the equation: $2 + 11 + x = 21$ Solving for $x$: $13 + x = 21$ $x = 21 - 13 = 8$

Final values of the cards

The three numbers are 2, 8, and 11.

Would you like more details or further clarifications on this problem?

Here are 5 related questions you might find interesting:

1. How do you calculate the range if given three numbers?
2. How do you solve for a variable when given a mean?
3. What if the range of the numbers had been different? How would that change the solution?
4. What are other statistical measures besides mean and range?
5. How do the concepts of minimum, maximum, and range interact in sets with more than three numbers?

Tip: Always check if any information like the minimum or range can directly give you one of the unknown values.