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?
- 35
- 26
- 33
- 25
The Correct Option is D
Solution and Explanation
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.
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