The equation for the rental charge includes the following; a fixed rental fee, a charge for gas and charge for miles covered. If the fixed charge for rental is a, the charge for gas is b and the charge per mile is d, then the total rental charge would be;
Cost = a + b + d
For Rapid rental, this becomes
Cost = 40 + 15 + 0.25d
Cost = 55 + 0.25d
However for Capital cars, to rent the same car would cost;
Cost = 45 + 0.35d ( note that Capital charges 45 for rental and gas, so a + b = 45)
The cost per miles for the same car can be expressed as an equation of both expressions. That is;
[tex]\begin{gathered} 55+0.25d=45+0.35d \\ \text{Collect all like terms and you now have} \\ 55-45=0.35d-0.25d \\ 10=0.10d \\ \text{Divide both sides by 0.10} \\ 100=d \end{gathered}[/tex]Having calculated the value of d, we can now substitute this into the cost function to get the cost for each rental.
For Rapid Rental, the cost is;
[tex]\begin{gathered} \text{Cost}=55+0.25d \\ \text{Cost}=55+0.25(100) \\ \text{Cost}=55+25 \\ \text{Cost}=80 \end{gathered}[/tex]For Capital Cars, the cost is;
[tex]\begin{gathered} \text{Cost}=45+0.35d \\ \text{Cost}=45+0.35(100) \\ \text{Cost}=45+35 \\ \text{Cost}=80 \end{gathered}[/tex]Hence the cost in both rental services is $80
