The temperatures $ f^\circ \text{F}$ and $ c^\circ \text{C}$ are equal when $ f \equal{} \frac {9}{5}c \plus{} 32$. What temperature is the same in both $ ^\circ \text{F}$ and $ ^\circ \text{C}$?
1. Let \( x \) be the temperature that is the same in both Fahrenheit and Celsius. Therefore, we have:
   \[
   x^\circ \text{F} = x^\circ \text{C}
   \]
2. According to the given formula for converting Celsius to Fahrenheit:
   \[
   f = \frac{9}{5}c + 32
   \]
   Since \( f = x \) and \( c = x \), we substitute \( x \) for both \( f \) and \( c \):
   \[
   x = \frac{9}{5}x + 32
   \]
3. To solve for \( x \), we first isolate the term involving \( x \) on one side of the equation. Subtract \(\frac{9}{5}x\) from both sides:
   \[
   x - \frac{9}{5}x = 32
   \]
4. Combine the terms on the left-hand side. Note that \( x \) can be written as \(\frac{5}{5}x\):
   \[
   \frac{5}{5}x - \frac{9}{5}x = 32
   \]
   Simplify the left-hand side:
   \[
   \frac{5x - 9x}{5} = 32
   \]
   \[
   \frac{-4x}{5} = 32
   \]
5. To solve for \( x \), multiply both sides of the equation by \(-\frac{5}{4}\):
   \[
   x = 32 \times -\frac{5}{4}
   \]
   \[
   x = -40
   \]

The final answer is \(\boxed{-40}\).