Chemistry Question: Isomerization Reactions and Differential Equations

My math methods class has a chemistry problem on it that I don't understand. We were given this as an example set of reactions:
A -> B
B -> A
B + B -> C
Which yields the set of differential equations:
A'[t] = -A[t] + B[t]
B'[t] = +A[t] - B[t] - B[t]^2
C'[t] = +B[t]^2
This makes sense, all the terms balance out, and we notice that B + B becomes B[t]^2 as a differential equation.

For homework, we are given this set of reactions:
A -> B
B -> A
A + B -> C

The term for C'[t] seems pretty obvious, C'[t] = A[t]B[t]. For the A->B reaction, we see that B'[t] has at least the term +A[t], and to balance this, A'[t] must have the term -A[t]. For the B->A reaction, it works the same way, so A'[t] has the term +B[t] added and B'[t] has the term -B[t]. However, I don't know how to balance the A[t]B[t] term. What do I subtract it from? Help?