Eggs in a basket are counted in fours, leaving 3 over, and in fives, leaving 4 over. What is the least number of eggs the basket can hold?

Explanation

1. 01

   $x \equiv 3 \pmod{4}$ and $x \equiv 4 \pmod{5}$ both say $x \equiv -1$: one more egg would make whole fours and whole fives.

2. 02

   So $x + 1$ is a multiple of 20, and the least is $x = 19$.