Contest math

1. We know that 7a=b, 8b=c, and 9c=d. If d=2016, what is a?

2. For some numbers $p$ and $q$, the solution of the system of equations

 $\begin{align*} x+3y &= 5 , \\ 3x+py &= 7 \end{align*}$
is $(x,y)=(-1,q)$. What is the value of $p$?

3. If $\frac{x}{2} + \frac{y}{3} = 1$ and $\frac{x}{4} + \frac{2y}{3} = -1$, what is the value of the sum of $x$ and $y$?

4. Let a, b, c, and d be positive integers. We know that

 $\begin{align*} a+b&=kc,\\ b+c&=kd,\\ c+d&=ka,\\ d+a&=kb. \end{align*}$
Find the maximum of $\dfrac ab + \dfrac bc + \dfrac cd + \dfrac da.$