When Phil and Shelley stand on a scale together, the scale reads $151$ pounds. When Shelley and Ryan stand on the same scale together, the scale reads $132$ pounds. When Phil and Ryan stand on the same scale together, the scale reads $115$ pounds. Find the number of pounds Shelley weighs.
1. Define the variables for the weights of Phil, Shelley, and Ryan:
   \[
   p = \text{Phil's weight}, \quad s = \text{Shelley's weight}, \quad r = \text{Ryan's weight}
   \]

2. Write down the given equations based on the problem statement:
   \[
   p + s = 151 \quad \text{(1)}
   \]
   \[
   s + r = 132 \quad \text{(2)}
   \]
   \[
   p + r = 115 \quad \text{(3)}
   \]

3. Add all three equations together:
   \[
   (p + s) + (s + r) + (p + r) = 151 + 132 + 115
   \]
   Simplify the left-hand side:
   \[
   2p + 2s + 2r = 398
   \]
   Divide both sides by 2:
   \[
   p + s + r = 199 \quad \text{(4)}
   \]

4. Use equation (4) to solve for Shelley's weight \(s\). From equation (3), we have:
   \[
   p + r = 115
   \]
   Substitute \(p + r\) from equation (3) into equation (4):
   \[
   s = 199 - (p + r)
   \]
   \[
   s = 199 - 115
   \]
   \[
   s = 84
   \]

The final answer is \(\boxed{84}\).