21. $r$ and $s$ are integers such that
$$
3 r \geq 2 s-3 \text { and } 4 s \geq r+12 \text {. }
$$

What is the smallest possible value of $r / s$ ?
Solution:
$1 / 2$
We simply plot the two inequalities in the $s r$-plane and find the lattice point satisfying both inequalities such that the slope from it to the origin is as low as possible. We find that this point is $(2,4)$ (or $(3,6)$ ), as circled in the figure, so the answer is $2 / 4=1 / 2$.