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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**.

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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.

The minimum of the set of number cards is 2. The range of the cards is 9. The mean of the cards is 7. Find the values of the number cards.

Learn how to find the values of three number cards when given the minimum (2), range (9), and mean (7). This problem uses core mathematical concepts such as mean and range, suitable for students in grades 6-8.

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