Let us make an equation for demand as a function of price.
d(p)=(48,150), (50, 146)
So the rate of change is (146-150)/(50-48)=-4/2=-2. So the slope of this function is -2 and the initial value. Now we have:
d(p)=-2p+b and we know we have the point (50,146)
146=-2(50)+b
146=-100+b
246=b so
d(p)=-2p+246
Revenue is price times demand so:
r(p)=p*d(p)
r(p)=p(-2p+246)
r(p)=-2p^2+246p
Revenue is maximized when dr/dp=0
dr/dp=-4p+246
dr/dp=0 when 4p=246
p=$61.50
So a rental charge of $61.50 maximizes revenue.
...
In case you were curious...
revenue max=r(61.5)=$7564.50
cars rented at this rad=d(61.5)=123 cars
