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60 people attend a game night. Everyone chooses to play chess, a two-player game, or cribbage, a four-player game. All 60 people are playing either chess or cribbage.

There are 3 more games of cribbage being played than games of chess being played. How many of each game are being played

Respuesta :

Answer: 8 chess matches and 11 cribbage matches.

Step-by-step explanation:

60 people, 4 people play a match of cribbage, so if theres 3 more  matched than chess we can subtract that from the total 60 to get the answer. 3x4=12 60-12=48, 2 people per chess game and 4 people per cribbage game add them 6, 48 divided by 6 since its an even amount now, 48/6=8 add 8 matched to the remaining 3 for the cribbage.

8 chess games are being played while 11 cribbage games are being played.

Let x represent the number of chess games and y represent the number of cribbage games.

Since there are 60 people, chess is a two-player game and cribbage is a four-player game, hence:

2x + 4y = 60  (1)

There are 3 more games of cribbage than games of chess, hence:

y = x + 3

-x + y = 3    (2)

Solving equations 1 and 2 simultaneously gives:

x = 8, y = 11

Therefore 8 chess games are being played while 11 cribbage games are being played.

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