Question

Alan, Bill, and Calvin are palying a game with collectible cards. At the moment, Alan has 11 less than 2 1/2 time the number of cards Bill has. Calvin has 1 more than 1 1/2 time 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 has is ______. If Alan, Bill, and Calvin ave all the cards in the deck, then the deck has ______ cards.

Please answer.

Answer 1

Let x = the number of cards Bill has, then

The number of cards Allan has =
$\frac{5}{2} x - 11 \: and \\ \\ the \: number \: of \: cards \: calvin \: has \: = \\ \: \frac{11}{2} x + 1$
The number of cards Alan has = The number of Calvins cards, so

$\frac{5}{2}x - 11 = \frac{11}{2}x + 1 \\ \\ which \: means \\ - 12 = 3x \: \: so \\ x = - 4 \\ \\ bill \: has \: - 4 \: cards \\ \\ allan \: has \\ \frac{5}{2} \times - \frac{4}{1} - 11 = - - 10 - 11 = - 21 \: cards \\ \\ calvin \: has \: \frac{11}{2} \times - \frac{4}{1} + 1 = - 22 + 1 = - 21 \: cards \\ \\ the \: deck \: has \: - 21 - 21 - 4 = - 46 \: \: cards \\ \\ this \: was \: not \: a \: good \: problem$