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

Mathematics Questions

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

Short Answer

To solve the problem, define variables for the number of chess (x) and cribbage games (y) and set up the equations: 2x + 4y = 60 and y = x + 3. Solving these equations simultaneously results in 8 chess games and 11 cribbage games being played.

Step-by-Step Solution

Step 1: Define the Variables

Begin by establishing your variables to represent the games being played. Let x be the number of chess games and y be the number of cribbage games. This will help in forming equations based on the problem statement regarding the total number of games.

Step 2: Set Up the Equations

From the problem, create two equations based on the number of players and the games. First, since chess is a two-player game and cribbage is a four-player game, you can express the total number of players as:

2x + 4y = 60 (Equation 1)

Additionally, since there are three more games of cribbage than chess, you can state:

y = x + 3 (Equation 2)

Step 3: Solve the Equations

Now, solve the two equations simultaneously to find the values of x and y. Substitute Equation 2 into Equation 1:

Replace y in Equation 1 to get 2x + 4(x + 3) = 60.
Simplify to find x = 8 (chess games).
Substituting back gives y = 11 (cribbage games).

Thus, you find that 8 chess games and 11 cribbage games are being played.

If 60 people attend a game night and everyone plays …