A basketball team played 74 games. They won 34 more than they lost.
How many games did they win?
How many games did they lose?
Let's assume the number of games the team lost is x.
The number of games they won would then be x + 34.
Since they played a total of 74 games, we can write the equation:
x + (x + 34) = 74
Combining like terms:
2x + 34 = 74
Subtracting 34 from both sides:
2x = 40
Dividing both sides by 2:
x = 20
So the team lost 20 games and won 20 + 34 = <<20+34=54>>54 games. Answer: \boxed{54}.
Let's solve the problem step-by-step:
Step 1: Let's assume the number of games they lost as 'x'.
Step 2: According to the problem, they won 34 more games than they lost, which means they won 'x + 34' games.
Step 3: The total number of games they played is given as 74.
Step 4: So we can write the equation as 'x + (x + 34) = 74'.
Step 5: Now, we can solve the equation to find the value of 'x':
2x + 34 = 74
Step 6: Subtracting 34 from both sides of the equation gives us:
2x = 74 - 34
2x = 40
Step 7: Dividing both sides of the equation by 2 gives us:
x = 40 / 2
x = 20
Therefore, they lost 20 games.
Step 8: Now, to find the number of games they won, we can substitute the value of 'x' into the equation:
Number of games won = x + 34
Number of games won = 20 + 34
Number of games won = 54
Therefore, they won 54 games.
Conclusion: The basketball team won 54 games and lost 20 games.
To find the number of games the basketball team won and lost, we can set up a system of equations.
Let's assume that the number of games they won is "W" and the number of games they lost is "L". According to the given information, we can set up the following equations:
Equation 1: W + L = 74 (the total number of games played)
Equation 2: W = L + 34 (they won 34 more games than they lost)
To solve this system of equations, we can use the method of substitution.
Step 1: Substitute the value of W from Equation 2 into Equation 1.
(L + 34) + L = 74
Combine like terms:
2L + 34 = 74
Step 2: Subtract 34 from both sides of the equation:
2L = 74 - 34
2L = 40
Step 3: Divide both sides of the equation by 2:
L = 40 / 2
L = 20
So, the team lost 20 games.
Step 4: Substitute the value of L into Equation 2 to find the value of W:
W = 20 + 34
W = 54
Therefore, the team won 54 games.
In summary:
- The basketball team won 54 games.
- The basketball team lost 20 games.