Let the price of the train set without any discounts be \( x \).
In the first month, the train set is advertised for 50% off with the purchase of a $10 membership card. The price after the discount is:
\[ \text{Discounted price} = x - 0.5x = 0.5x \]
The total cost for the train set and membership card in this month is:
\[ \text{Total cost} = 0.5x + 10 \]
In the second month, the train set is advertised for 75% off with the purchase of a $20 membership card. The price after the discount is:
\[ \text{Discounted price} = x - 0.75x = 0.25x \]
The total cost for the train set and membership card in this month is:
\[ \text{Total cost} = 0.25x + 20 \]
According to the problem, Bonnie realized that the total prices did not change, which gives us:
\[ 0.5x + 10 = 0.25x + 20 \]
Now, we'll solve this equation for \( x \).
First, isolate \( x \):
\[ 0.5x - 0.25x = 20 - 10 \]
\[ 0.25x = 10 \]
Now, solve for \( x \):
\[ x = \frac{10}{0.25} = 40 \]
Thus, the price of the train set without any discounts is \(\boxed{40}\).