A diesel car

A diesel car costs $2599 more than an unleaded petrol car and travels an average of 25,000km per year. Diesel petrol has a consumption rate of 7.4L per 100km and costs $1.39 per liter. Unleaded gasoline has a consumption rate of 8.5L per 100km and costs $1.65 per liter. How many months would it take to justify buying the more expensive diesel car financially?

Correct answer:

x =  34

Step-by-step explanation:

$$\begin{gathered} m=25000/12=\frac{6250}{3}=2083\frac{1}{3}\doteq 2083.3333\text{km/m} \\ {c}_1=7.4\cdot 1.39/100\doteq 0.1029\text{USD/km} \\ {c}_2=8.5\cdot 1.65/100=\frac{561}{4000}\doteq 0.1403\text{USD/km} \\ {m}_1=m\cdot c_1=2083.3333\cdot 0.1029=\frac{5143}{24}=214\frac{7}{24}\doteq 214.2917\text{USD/m} \\ {m}_2=m\cdot c_2=2083.3333\cdot 0.1403=\frac{4675}{16}=292\frac{3}{16}=292.1875\text{USD/m} \\ d=m_2-m_1=292.1875-214.2917=\frac{3739}{48}=77\frac{43}{48}\doteq 77.8958\text{USD/m} \\ {x}_1=2599/d=2599/77.8958\doteq 33.3651 \\ x=\lceil x_1\rceil =\lceil 33.3651\rceil =34 \end{gathered}$$

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