jmc

Suppose that there are $a$ ants of Species A and $b$ ants of Species B on Day 0. We thus have that $a+b=30$. Notice that on Day 1, there will be $2a$ ants of Species A, on Day 2, there will be $2(2a)=4a$ ants of Species A, and on Day 3, there will be $2(4a)=8a$ ants of Species A, etc. Following this line of reasoning, on Day 5, there will be $2^{5}a$ ants of Species A and $3^{5}b$ ants of Species B, meaning that $32a+243b=3281$. We now solve this system of linear equations. We have that $32a+32b=960$, so $$\begin{array}{rl}(32a+243b)-(32a+32b)& =211b\\ & =3281-960\\ & =2321.\end{array}$$We then have $b=\frac{2321}{211}=11$. This means that $a=30-11=19$, and there are $32\cdot 19=\boxed{608}$ ants of Species A on Day 5.