Use Deductive problem solving please. $(50$ points$)$ Determine what the price of fuel in $($$$)/($m$^(3))$ needs to be in order to receive a $25\%$ return on investment when purchasing a car with an

optimum efficiency of $40\%.$ The budget car has an efficiency of $20\%.$ The cars operate on natural gas, where R$=0\mathrm{.}5182[$k$($J$)/($k$)$g$-$K$],$ and with a

lower heating value of $50,050[$k$($J$)/($k$)$g$].$ The fuel enters the engine at $100[$kPa$]$ and $300[$K$].$ The engine has a maximum net power output of $100$

$[$kW$].$ Based on initial cost quotes, the cost coefficient is $$(100)/($k$)$W and the exponent is $1\mathrm{.}7.$ The adiabatic flame temperature $($T$\_($H$))$ is $2,000[$K$]$T$\_($L$)300[$K$].$ Over its $15$ year life, the car overcomes an average force of $1,500[$N$]$ while traveling $20,000[$kilometers

each year$].$ Tip: During your calculations, use algebra to solve for operating costs from the definition of cost per unit of fuel and substitute in the

equation for savings.