Used cars

Peter plans to buy a used car:
the first car Renault Espace 2.0 dCi 16V Dynamique 2006, costs 2000 euros. It is 14 years old and has a combined diesel consumption of 8 liters. / 100 km. Diesel costs 1.1 euros/liter. How much will the car cost him to operate for the next 4 years if he drives 11,000 km a year? What is its annual cost?

The second car is younger and is on the gas Renault grand scenic 3 LPG 2010, costs 3700 euros. It is 10 years old and has a gas consumption of 10 liters/100 km. LPG costs 55 cents/liter. How much will the car cost it to operate in the next 4 years if it drives 11,000 km a year? What is its annual cost?

Neglect the prices of failures and MOT, EC and the consumption of petrol in a car on gas for starting and also the more expensive emission in a car on gas (the car actually passes the emission on gasoline and the emission on gas). Also, neglect the need to replace the LPG tank after 10 years about 250 euros. We must save 250/10 = 25 euros to replace the LPG gas tank every year for 10 years.

At what raid does the car start to pay for LPG? Compare cars

Correct answer:

x1 =  5872 Eur
r1 =  1468 Eur
x2 =  6120 Eur
r2 =  1530 Eur
z =  51515.1515 km

Step-by-step explanation:

a1=2000 l=11000 km q1=8 1.1/100=11125=0.088 eur/km s1=l q1=11000 0.088=968 Eur/r n=4 y s11=n s1=4 968=3872 Eur  x1=s11+a1=3872+2000=5872 Eur
r1=x1/n=5872/4=1468 Eur
a2=3700 q2=10 0.55/100=11200=0.055 Eur/km s2=l q2=11000 0.055=605 Eur/r  s22=n s2=4 605=2420 Eur  x2=s22+a2=2420+3700=6120 Eur
r2=x2/n=6120/4=1530 Eur
  z/100 8 1.1+a1=z/100 10 0.55+a2 z/100 8 1.1+2000=z/100 10 0.55+3700  3.3z=170000  z=51515.151515=51515.1515 km=5.152104 km

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