Simultaneous linear equations: TJC 2024 Promo Q2

Let $x$, $y$ and $z$ be the number of plates of chicken rice, duck rice and pork rice sold.

Total profit $=\$167.40$ $$\begin{aligned} &\Longrightarrow 50x+80y+110z=16740\\ &\Longrightarrow 5x+8y+11z=1674 \quad\text{(1)} \end{aligned}$$ Mr Chan earned $$28.80$ more in profit from the sale of pork rice than the chicken rice $$\begin{aligned} &\Longrightarrow 110z-50x=2880\\ &\Longrightarrow -5x+11z=288 \quad\text{(2)} \end{aligned}$$ Total number of plates of rice sold being $3$ times the plates of duck rice sold $$\begin{aligned} &\Longrightarrow x+y+z=3y\\ &\Longrightarrow x-2y+z=0 \quad\text{(3)} \end{aligned}$$ Solving (1), (2), (3), we have $x=81$, $y=72$, $z=63$

Mr Chan sold $81$ plates of chicken rice, $72$ plates of duck rice and $63$ plates of pork rice that day.