Answer
$\textbf{(a)}$ $\underline{\text{For Plan 1}}$ $C_1=195+0.15x$ .......(1)
$\underline{\text{ For Plan 2}}$ $C_2=270$ .......(2)
$\textbf{(b)}$
The plan $1$ is the cheaper one if the businessman drive $400$ miles and The plan $2$ is the cheaper one if the businessman drive $800$ miles.
$\textbf{(c)}$ The two plans cost will be the same at $500$ mile
Work Step by Step
$\textbf{(a)}$ $\underline{\text{For Plan 1}}$
The rent of the car for 3 days is $65\times 3=\$195$, in addition to $\$0.15$ per miles.
i.e the cost $C$ for $x$ miles, is
$C_1=195+0.15x$ .......(1)
$\underline{\text{ For Plan 2}}$
The rent of the car for 3 days is $90\times 3=\$270$.
i.e the cost $C$ for $x$ miles, is
$C_2=270$ .......(2)
$\textbf{(b)}$
$C_1(400)=195+0.15(400)=255$
$C_1(800)=195+0.15(800)=315$
$C_2(400)=270$
$C_2(800)=270$
i.e The plan $1$ is the cheaper one if the businessman drive $400$ miles and The plan $2$ is the cheaper one if the businessman drive $800$ miles.
$\textbf{(c)}$
The two plans cost will be the same at
$195+0.15x=270\Rightarrow 0.15x=75\Rightarrow x=500$ mile
