Environmentally 30731

Peter plans to buy a used seven-seater for a large family. The so-called van or MPV.

The first car Renault Espace 2.0 dCi 16V Dynamique 2006, costs 2000 euros + 350 euros registration for Slovak brands, imported from Italy. It is 14 years old and has a combined diesel consumption of 8 liters per 100 km. Diesel costs 1.1 euros / liter. How much will the car cost for the next four years if it drives 10,000 km a year? What is its annual cost?

The second car is younger and powered by the C4 Grand Picasso 2010. It costs 4,500 euros. It is ten years old and has a diesel consumption of only 5.5 liters / 100 km, so it is more environmentally friendly and probably has lower operating costs at higher ramps. How much will the car cost for the next four years if it drives 10,000 km a year? What is its annual fee?

Neglect the prices of failures and MOT, EC, various prices of UGS insurance, etc.

During which raid does the younger C4 grand Picasso start paying off? Compare cars

Correct answer:

x₁ =  5870 Eur
r₁ =  1467.5 Eur
x₂ =  6920 Eur
r₂ =  1730 Eur
z =  78181.8182 km

Step-by-step explanation:

$$\begin{gathered} a_1=2000+350=2350\text{Eur} \\ l=10000\text{km} \\ d=1.1\text{Eur/l} \\ {q}_1=8\cdot d/100=8\cdot 1.1/100=\frac{11}{125}=0.088\text{eur/km} \\ {s}_1=l\cdot q_1=10000\cdot 0.088=880\text{Eur/r} \\ n=4\text{y} \\ {s}_{11}=n\cdot s_1=4\cdot 880=3520\text{Eur} \\ {x}_1=s_{11}+a_1=3520+2350=5870\text{Eur} \end{gathered}$$

$r_1=x_1/n=5870/4=1467.5\text{Eur}$

$$\begin{gathered} a_2=4500\text{Eur} \\ {q}_2=5.5\cdot d/100=5.5\cdot 1.1/100=\frac{121}{2000}=0.0605\text{Eur/km} \\ {s}_2=l\cdot q_2=10000\cdot 0.0605=605\text{Eur/r} \\ {s}_{22}=n\cdot s_2=4\cdot 605=2420\text{Eur} \\ {x}_2=s_{22}+a_2=2420+4500=6920\text{Eur} \end{gathered}$$

$r_2=x_2/n=6920/4=1730\text{Eur}$

$$\begin{gathered} z/100\cdot 8\cdot d+a_1=z/100\cdot 5.5\cdot d+a_2 \\ z/100\cdot 8\cdot 1.1+2350=z/100\cdot 5.5\cdot 1.1+4500 \\ 2.75z=215000 \\ z=\frac{215000}{2.75}=78181.81817934 \\ z=78181.818179=78181.8182\text{km} \end{gathered}$$

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