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 \(\dfrac ab + \dfrac bc + \dfrac cd + \dfrac da.\)
