Question $1[8]$

Mohammad purchased a Toyota Highlander Hybrid that consumes about $6$ L of gasoline a day, and the capacity of the fuel tank of a car is about $60L.$ Depending on the temperature in Saudi Arabia, the density of gasoline ranges from $0\mathrm{.}68$ to $0\mathrm{.}78\frac{kg}{L},$ and its lower heating value is about $44,000K\frac{j}{k}g.$ He refuels the car twice per month with Octane$-91$ at an expense of SAR $250.$ He also needs to spend around SAR $7000$ for maintenance every year. Suppose Mohammad has an offer to replace the existing engine with a nuclear engine powered by uranium $(U-235).$ Toyota offers to equip the engine with $50g$ of the nuclear fuel U$-235.$ One $kg$ of U$-235$ releases $6\mathrm{.}73{10}^{10}kJ$ of heat. If fuel efficiency of the nuclear$-$engine is $98\%,$ answer the followings:

$($i$)$ Estimate a period of refueling his new car for the average driving conditions. $[4]$

$($ii$)$ The cost of the nuclear engine is SAR $85,000.$ Is it a reasonable price? Why? $[4]$