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Let's break down and solve the problem step by step:

### Information given:
- In the first half of the year:
  - The team won 60% of the games it played.
  - Let \( x \) be the number of games played in the first half.

- In the second half of the year:
  - The team played 20 games and won 3 of them.

- Overall, the team won 50% of the games played over the entire year.

### Step 1: Total games played and total wins
- The total number of games played last year = \( x \) (first half) + 20 (second half).
- The total number of games won last year = 60% of \( x \) (first half) + 3 (second half).

### Step 2: Set up the equation for overall win percentage
The team won 50% of all games, so the equation for total wins is:
\[
\frac{0.6x + 3}{x + 20} = 0.5
\]

### Step 3: Solve for \( x \)
Multiply both sides by \( x + 20 \):
\[
0.6x + 3 = 0.5(x + 20)
\]
Simplify the right-hand side:
\[
0.6x + 3 = 0.5x + 10
\]

Now, move the terms involving \( x \) to one side:
\[
0.6x - 0.5x = 10 - 3
\]
\[
0.1x = 7
\]
Solve for \( x \):
\[
x = 70
\]

### Step 4: Calculate the total number of games
The total number of games played last year is:
\[
x + 20 = 70 + 20 = 90
\]

Thus, the total number of games the team played last year is **90**.

---

Would you like further clarification on any step? Here are some related questions you could explore:

1. How would the answer change if the team won a different percentage of games in the second half?
2. What if the team won 70% of its games in the first half instead of 60%?
3. How does altering the number of games in the second half affect the overall win percentage?
4. Can we verify the solution by plugging the value of \( x \) back into the equation?
5. What happens if the team had played fewer games in the second half?

**Tip**: Always define the variables clearly and use them consistently throughout the problem-solving process.

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?

Solve an algebra problem where a team won 60% of its games in the first half, played 20 games in the second half, and overall won 50% of its games last year. Detailed step-by-step solution to find the total number of games played.

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