Narlow made a basket using three pieces of wicker. The first piece was \( \theta \) in. long, the second was \( 1 / 2 \) in \( 3 / 4 \) onger than the frist, and the third was \( 8 / 4 \) in shonter than the second. How much wicker did she use?

Let's break down the problem step by step. 1. **Identify the lengths of each piece of wicker:** - The first piece is \( \theta \) inches long. - The second piece is \( \frac{1}{2} \) inches longer than the first piece. Therefore, its length can be expressed as: \[ L_2 = \theta + \frac{1}{2} \] - The third piece is \( \frac{8}{4} \) inches shorter than the second piece. Since \( \frac{8}{4} = 2 \), the length of the third piece is: \[ L_3 = L_2 - 2 = \left(\theta + \frac{1}{2}\right) - 2 \] Simplifying this gives: \[ L_3 = \theta + \frac{1}{2} - 2 = \theta - \frac{3}{2} \] 2. **Calculate the total length of wicker used:** The total length \( L \) of wicker used is the sum of the lengths of the three pieces: \[ L = L_1 + L_2 + L_3 \] Substituting the expressions we found: \[ L = \theta + \left(\theta + \frac{1}{2}\right) + \left(\theta - \frac{3}{2}\right) \] 3. **Combine the terms:** \[ L = \theta + \theta + \frac{1}{2} + \theta - \frac{3}{2} \] \[ L = 3\theta + \frac{1}{2} - \frac{3}{2} \] \[ L = 3\theta - 1 \] Thus, the total length of wicker used by Narlow is: \[ \boxed{3\theta - 1} \text{ inches} \]