Let \( x \) represent the amount the school spent on the winter dance last year.
According to the information provided, the school plans to spend twice the amount it did last year, minus the cost of the disco ball. The equation representing the total spending for this year is:
\[ 2x - 150 = 1500 \]
To solve for \( x \), first, we can add 150 to both sides of the equation:
\[ 2x - 150 + 150 = 1500 + 150 \]
This simplifies to:
\[ 2x = 1650 \]
Next, divide each side by 2:
\[ x = \frac{1650}{2} = 825 \]
Thus, the amount the school spent last year on the winter dance was $825.