Ans: $43$
Let $x$ and $y$ be the number of elderly patients and non-elderly patients on that day respectively.
Let $x$ and $y$ be the number of elderly patients and non-elderly patients on that day respectively.
$\left\{ \begin{array}{ll}
x+y= 67 & \ldots \unicode{x2460} \\
120x+160y = 9000 & \ldots \unicode{x2461}
\end{array} \right.$
From $\unicode{x2460}$, we have
$\begin{array}{rcl}
x+y & = & 67 \\
y & = & 67-x \ \ldots \unicode{x2462}
\end{array}$
Sub. $\unicode{x2462}$ into $\unicode{x2461}$, we have
$\begin{array}{rcl}
120x + 160(67-x) & = & 9000 \\
120x + 10720 – 160x & = & 9000 \\
-40x & = & -1720 \\
x & = & 43
\end{array}$
Therefore, there are $43$ elderly patients on that day.
