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Let's break down the problem and solve it step by step.

1. **Understanding the Problem**:
   - In the first half, the team won 60% of its games.
   - In the second half, the team played 20 games and won 3.
   - The team's overall win rate for the year was 50%.
   - We need to determine the total number of games played last year.

2. **Define Variables**:
   - Let \( x \) be the number of games the team played in the first half of the year.
   - In the first half, the number of games won is \( 0.6x \).
   - The total number of games played is \( x + 20 \) (where 20 is the games played in the second half).

3. **Set Up the Equation**:
   - The total number of wins over the year is \( 0.6x + 3 \).
   - Since the team won 50% of the games it played, the equation becomes:
     \[
     \frac{0.6x + 3}{x + 20} = 0.5
     \]

4. **Solve the Equation**:
   - Cross-multiply to get:
     \[
     0.6x + 3 = 0.5(x + 20)
     \]
   - Simplify and solve for \( x \):
     \[
     0.6x + 3 = 0.5x + 10
     \]
     \[
     0.1x = 7
     \]
     \[
     x = 70
     \]

5. **Find the Total Number of Games**:
   - Total games played = \( x + 20 \) = \( 70 + 20 = 90 \).

### Final Answer:
The team played a total of **90 games** last year.

Would you like a more detailed breakdown or have any questions? Here are some related questions to deepen your understanding:

1. What would the team's win rate be if they won 5 games in the second half instead of 3?
2. How many games would the team need to win in the first half to maintain a 50% win rate if they played only 15 games in the second half?
3. If the team's overall win rate was 60%, how would the total number of games change?
4. How many games did the team lose in total last year?
5. What is the ratio of games won to games lost throughout the entire year?

**Tip**: When dealing with percentage problems, defining variables for unknown quantities can simplify setting up equations for a solution.

In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?

Learn how to solve a win percentage problem where a team won 60% of games in the first half, 3 out of 20 in the second half, and had an overall win rate of 50%. This problem covers algebra, percentages, and linear equations, suitable for students in Grades 9-11.

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