Last month a pet store sold three times as many cats as dogs. If the store had sold the same number of cats but eight more dogs, it would have sold twice as many cats as dogs. How many cats did the pet store sell last month?
1. Let \( x \) be the number of dogs sold last month.
2. According to the problem, the number of cats sold is three times the number of dogs sold. Therefore, the number of cats sold is \( 3x \).
3. If the store had sold the same number of cats but eight more dogs, the number of dogs would be \( x + 8 \).
4. Under this new condition, the number of cats sold would be twice the number of dogs sold. Therefore, we can set up the equation:
   \[
   3x = 2(x + 8)
   \]
5. Solve the equation for \( x \):
   \[
   3x = 2(x + 8)
   \]
   \[
   3x = 2x + 16
   \]
   \[
   3x - 2x = 16
   \]
   \[
   x = 16
   \]
6. Substitute \( x = 16 \) back into the expression for the number of cats sold:
   \[
   3x = 3 \times 16 = 48
   \]

The final answer is \( \boxed{48} \).