Question

Alan, Bill, and Calvin are playing a game with collectible cards. At the moment, Alan has 11 less than three times the number of cards Bill has, and Calvin has 1 more than two 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 ______.

A) Bill has 13 cards; Alan and Calvin each have 26 cards.
B) Bill has 15 cards; Alan and Calvin each have 28 cards.
C) Bill has 17 cards; Alan and Calvin each have 30 cards.
D) Bill has 19 cards; Alan and Calvin each have 32 cards.
E) None of the above.

Answer 1

Bill has 12 cards; Alan and Calvin each have 25 cards. The correct answer is C) Bill has 17 cards; Alan and Calvin each have 30 cards.

Step-by-step explanation:

To solve this problem, let's assign a variable to the number of cards Bill has.

Let's say that Bill has x cards.

According to the information given, Alan has 11 less than three times the number of cards Bill has, so Alan has 3x - 11 cards.

Calvin has 1 more than two times the number of cards Bill has, so Calvin has 2x + 1 cards.

Since Alan and Calvin have the same number of cards, we can set up an equation:

3x - 11 = 2x + 1

Simplifying the equation, we get:

x = 12

Therefore, Bill has 12 cards.

The number of cards Alan and Calvin have is:

Alan: 3x - 11 = 3(12) - 11 = 36 - 11 = 25

Calvin: 2x + 1 = 2(12) + 1 = 24 + 1 = 25

So, Bill has 12 cards and Alan and Calvin each have 25 cards. Therefore, the correct answer is option C) Bill has 17 cards; Alan and Calvin each have 30 cards.