First, let's calculate the cost of the dress for Julie.
The original price of the dress is \(39.99\).
Julie buys the dress at a 10% discount. The discount can be calculated as follows: \[ \text{Discount} = 0.10 \times 39.99 = 3.999 \]
Now, subtract the discount from the original price to find the sale price for Julie: \[ \text{Sale Price for Julie} = 39.99 - 3.999 = 35.991 \]
Next, let's calculate the cost of the dress for Mindy.
Mindy buys the dress at a 20% discount. The discount is: \[ \text{Discount} = 0.20 \times 39.99 = 7.998 \]
Now, subtract the discount from the original price to find the sale price for Mindy: \[ \text{Sale Price for Mindy} = 39.99 - 7.998 = 31.992 \]
Now, we can find out how much more Julie spent than Mindy: \[ \text{Difference} = \text{Sale Price for Julie} - \text{Sale Price for Mindy} \] \[ \text{Difference} = 35.991 - 31.992 = 3.999 \]
Rounding this to the nearest whole number gives us \(4\).
Therefore, Julie spent $4 more than Mindy.
So the final answer is: \[ \boxed{4} \]