Question

In a chess tournament, a player earns 5 points for wins, and loses 2 points for losses. If a player played 30 games of chess and scored 94 points, how many wins and losses did the player have?

Answer 1

To find out how many wins and losses the player had in a chess tournament, we can set up a system of equations using the number of games played and the total score. Solving this system will give us the values of wins and losses.

Step-by-step explanation:

To solve this problem, let's assign variables to the number of wins and losses. Let's say the number of wins is represented by x, and the number of losses is represented by y. The player earns 5 points for each win and loses 2 points for each loss.

According to the information given, we can set up the following system of equations:

x + y = 30 (since the player played 30 games)

5x - 2y = 94 (since the player scored 94 points)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From the first equation, we can express y in terms of x:

y = 30 - x

Substituting this expression for y into the second equation, we get:

5x - 2(30 - x) = 94

Simplifying the equation, we have:

5x - 60 + 2x = 94

7x - 60 = 94

7x = 154

x = 22

Substituting the value of x back into the first equation, we get:

22 + y = 30

y = 8

Therefore, the player had 22 wins and 8 losses.