Let's denote the original amount of money the man had as \( x \).
1. **Loses 25% of his money**:
After losing 25% of his money, he is left with \( 0.75x \).
2. **Spends 20% of the rest**:
After spending 20% of the remaining money, he has \( 0.8 \times 0.75x \) left.
According to the problem, he has $10,200 left after these expenses.
So, we have the equation:
\[ 0.8 \times 0.75x = 10,200 \]
Let's solve for \( x \):
\[ 0.8 \times 0.75x = 10,200 \]
\[ 0.6x = 10,200 \]
\[ x = \frac{10,200}{0.6} \]
\[ x = 17,000 \]
Therefore, the man originally had $17,000.
