Question

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 be 133, how many cards does B have?

• A. 35
• B. 26
• C. 33
• D. 25

Answer 1

The Correct Option is D

Card Distribution Problem Analysis

1. Define Variables: 

Let A, B, C, D, and E represent the number of cards each person has.

2. Translate the Statements into Equations:

Statement 1: "If you give me three cards, you will have as many as E has."

B - 3 = E (Equation 1)

Statement 2: "If I give you three cards, you will have as many as D has."

B + 3 = D (Equation 2)

Statement 3: "A and B together have 10 cards more than what D and E together have."

A + B = D + E + 10 (Equation 3)

Statement 4: "B has two cards more than what C has."

B = C + 2 (Equation 4)

Statement 5: "The total number of cards is 133."

A + B + C + D + E = 133 (Equation 5)

3. Express All Variables in Terms of B:

From (Equation 1): E = B - 3

From (Equation 2): D = B + 3

From (Equation 4): C = B - 2

Substitute D, E, and C into (Equation 3):

Substitute into: A + B = (B + 3) + (B - 3) + 10

A + B = 2B + 10

A = B + 10

4. Substitute All Variables into (Equation 5):

Substitute A = B + 10, C = B - 2, D = B + 3, and E = B - 3 into (Equation 5):

(B + 10) + B + (B - 2) + (B + 3) + (B - 3) = 133

Simplify:

5B + 8 = 133

5B = 125

B = 25

Final Answer:

The number of cards D has is 25.