Solve. \( \begin{array}{r}\frac{z}{32}+\frac{5}{8}=\frac{13}{16} \\ z=46 \\ z=13 \\ z=1 \\ z\end{array} \)

To solve the equation \( \frac{z}{32} + \frac{5}{8} = \frac{13}{16} \), we first need to isolate \( z \). 1. Start by subtracting \( \frac{5}{8} \) from both sides: \[ \frac{z}{32} = \frac{13}{16} - \frac{5}{8} \] 2. To subtract the fractions, we need a common denominator. The least common denominator for \( 16 \) and \( 8 \) is \( 16 \): \[ \frac{5}{8} = \frac{10}{16} \] So we have: \[ \frac{z}{32} = \frac{13}{16} - \frac{10}{16} = \frac{3}{16} \] 3. Now we multiply both sides by \( 32 \) to solve for \( z \): \[ z = 32 \cdot \frac{3}{16} = 32 \cdot \frac{3}{16} = 2 \cdot 3 = 6 \] So, the solution is \( z = 6 \). To summarize our findings, none of the options \( z=46 \), \( z=13 \), or \( z=1 \) are correct; the actual answer is \( z=6 \).