Respuesta :

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.

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