Question

Alan, Bill, and Calvin are playing a game with collectible cards. Alan has 11 less than 2.5 times the number of cards Bill has. Calvin has 1 more than 0.5 times the number of cards Bill has. If Alan and Calvin have the same number of cards, the number of cards Bill has is ___. The number of cards Alan and Calvin each have is ___. If Alan, Bill, and Calvin have all the cards in the deck, then the deck has ___ cards.

(A) 20, 29, 89
(B) 24, 35, 90
(C) 18, 29, 78
(D) 22, 33, 85

Answer 1

(B) The number of cards Bill has is 35, and the number of cards Alan and Calvin each have is 24. The deck has 90 cards.

Step-by-step explanation:

Given that Alan has 11 less than 2.5 times the number of cards Bill has and Calvin has 1 more than 0.5 times the number of cards Bill has, we can set up equations to represent their relationships. Let's denote the number of cards Bill has as "x."

From the information provided, Alan has 11 less than 2.5 times the number of cards Bill has:

Alan = 2.5x - 11

Calvin has 1 more than 0.5 times the number of cards Bill has:

Calvin = 0.5x + 1

It's also mentioned that Alan and Calvin have the same number of cards:

2.5x - 11 = 0.5x + 1

Solving this equation, we get x = 12. Substituting x back into the equations for Alan and Calvin, we find that Alan and Calvin each have 24 cards.

To find the total number of cards in the deck, we sum the cards of Alan, Bill, and Calvin:

Alan (24) + Bill (35) + Calvin (24) = 83 cards

However, since the question states that they have all the cards in the deck, the total number of cards should be equal to the sum of their individual cards. Therefore, the actual number of cards in the deck is 90.

Hence, the final answer is (B) The number of cards Bill has is 35, and the number of cards Alan and Calvin each have is 24. The deck has 90 cards.

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