Let \( x \) be the original price of the skirt.
Since Jade buys both the blouse and skirt for \( \frac{3}{4} \) of their original price, the total cost is \( \frac{3}{4} \) of the sum of the original prices.
The equation representing the situation is:
\[ \frac{3}{4} (18 + x) = 31.50 \]
Now, let's solve for \( x \) using the Distributive Property:
\[ \frac{3}{4} \times 18 + \frac{3}{4} \times x = 31.50 \]
\[ \frac{54}{4} + \frac{3}{4}x = 31.50 \]
\[ 13.50 + \frac{3}{4}x = 31.50 \]
Subtract 13.50 from both sides:
\[ \frac{3}{4}x = 18 \]
Now, multiply both sides by \( \frac{4}{3} \) to solve for \( x \):
\[ x = 24 \]
So, the original price of the skirt is $24.
