Question

A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment, while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got?

• A. 28
• B. 41
• C. 29
• D. 35
• E. 31

Hint:

Translate word problems into equations step by step. Use variables for unknowns and solve systematically.

Answer 1

The Correct Option is A

Step 1: Let the number of cards with A, B, C, D, E be $a, b, c, d, e$.
Step 2: "If you give me 3 cards, you will have as many as I have at this moment": $b - 3 = a \implies b = a + 3$.
Step 3: "If D takes 5 cards from you, he will have as many as E has": $b - 5 = e$? Actually "D takes 5 cards from you" means B gives 5 to D, so D becomes $d + 5$, and that equals $e$: $d + 5 = e$.
Step 4: "A and C together have twice as many cards as E has": $a + c = 2e$.
Step 5: "B and D together also have the same number of cards as A and C taken together": $b + d = a + c$.
Step 6: Total: $a + b + c + d + e = 150$.
Step 7: From Step 4 and
Step 5: $b + d = 2e$.
Step 8: From
Step 2: $b = a + 3$. From
Step 3: $d = e - 5$.
Step 9: Substitute into $b + d = 2e$: $(a + 3) + (e - 5) = 2e \implies a - 2 + e = 2e \implies a - 2 = e \implies e = a - 2$.
Step 10: From
Step 3: $d = (a - 2) - 5 = a - 7$. From
Step 4: $a + c = 2(a - 2) = 2a - 4 \implies c = a - 4$.
Step 11: Total: $a + (a + 3) + (a - 4) + (a - 7) + (a - 2) = 150$. $5a - 10 = 150 \implies 5a = 160 \implies a = 32$.
Step 12: Then $c = a - 4 = 32 - 4 = 28$.
Step 13: Final Answer: 28.