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Let's break down the problem step by step, using algebra to represent the unknowns.

### Variables:
- Let \( A \), \( B \), \( C \), \( D \), and \( E \) represent the number of cards held by players A, B, C, D, and E respectively.

### Given conditions:

1. **A's statement:**
   - "If you (B) give me 3 cards, you will have as many as E has."
     \[
     B - 3 = E \quad \Rightarrow \quad B = E + 3 \tag{1}
     \]
   - "If I (A) give you 3 cards, you will have as many as D has."
     \[
     B + 3 = D \quad \Rightarrow \quad B = D - 3 \tag{2}
     \]

2. **Combined total of A and B vs D and E:**
   - "A and B together have 10 cards more than D and E together."
     \[
     A + B = D + E + 10 \tag{3}
     \]

3. **Relation between B and C:**
   - "B has 2 cards more than C."
     \[
     B = C + 2 \tag{4}
     \]

4. **Total number of cards:**
   - "The total number of cards is 133."
     \[
     A + B + C + D + E = 133 \tag{5}
     \]

### Solving the system of equations:

From equation \((1)\), we have \( B = E + 3 \).  
From equation \((2)\), we have \( B = D - 3 \).

Substitute these into equation \((3)\):
\[
A + B = D + E + 10
\]
Since \( B = E + 3 \), we have:
\[
A + (E + 3) = D + E + 10
\]
Simplifying:
\[
A + E + 3 = D + E + 10
\]
\[
A = D + 7 \tag{6}
\]

Now we have:
- \( A = D + 7 \) (from equation (6)),
- \( B = E + 3 \) (from equation (1)),
- \( B = D - 3 \) (from equation (2)),
- \( B = C + 2 \) (from equation (4)).

Let's substitute these into equation \((5)\) (the total number of cards):
\[
A + B + C + D + E = 133
\]
Using the relations for \( A \), \( B \), and \( C \):
\[
(D + 7) + B + (B - 2) + D + (B - 3) = 133
\]
Simplifying this:
\[
(D + 7) + B + (B - 2) + D + (B - 3) = 133
\]
\[
2D + 7 + 3B - 5 = 133
\]
\[
2D + 3B + 2 = 133
\]
\[
2D + 3B = 131 \tag{7}
\]

Now, substitute \( B = D - 3 \) (from equation (2)) into equation \((7)\):
\[
2D + 3(D - 3) = 131
\]
\[
2D + 3D - 9 = 131
\]
\[
5D - 9 = 131
\]
\[
5D = 140
\]
\[
D = 28
\]

Now that we have \( D = 28 \), substitute this back to find \( B \):
\[
B = D - 3 = 28 - 3 = 25
\]

Thus, **B has 25 cards**.

Would you like further clarification on this solution? Here are some additional questions that can extend your understanding:

1. How many cards does player A have?
2. How many cards does player C have?
3. How many cards does player E have?
4. Can you verify the total number of cards by adding up all individual counts?
5. How would the problem change if B had one card more than C instead of two?

**Tip:** When solving a system of equations, substituting early equations into later ones helps reduce the number of variables and simplifies the solution process.

A, B, C, D, and E play a game of cards. A says to B, 'If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has.' A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards is 133, how many cards does B have?

Learn how to solve a system of equations involving five players and 133 total cards. This detailed solution demonstrates algebraic reasoning, solving systems of linear equations, and interpreting complex word problems. Suitable for high school students in Grades 10-12.

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