Answer
$60\text{ days}$$
Work Step by Step
In part a) we built the system of equations:
$$\begin{cases}
y=50x+600\\
y=40x+1200.
\end{cases}$$
In order to find the value of $x$ so that the costs are equal, we graph the lines $y=50x+600$ and $y=40x+1200$ (see graph).
The intersection point appears to be $(60,3600)$.
We check the solution algebraically:
$$\begin{align*}
y&=50x+600\\
3600&\stackrel{?}{=}50(60)+600\\
3600&\stackrel{?}{=}3000+600\\
3600&=3600\checkmark\\\\
y&=40x+1200\\
3600&\stackrel{?}{=}40(60)+1200\\
3600&\stackrel{?}{=}2400+1200\\
3600&=3600\checkmark.
\end{align*}$$
The number of days after which the costs are equal is $x=60$.
