Question

Kyle bought a car then its value started decreasing by the same amount each year. After 3 years, it was worth 19300. After 7 years, it was worth13700. What was the initial value of the car?

1) $25000
2) $28000
3) $31000
4) $34000

Answer 1

To find the car's initial value, calculate the yearly depreciation and add the total depreciation after 3 years to the car's value at that time. The initial value of the car is $23,500.

Step-by-step explanation:

The question is about determining the initial value of a car given that its value depreciates by a consistent amount each year. We know that after 3 years, the car’s value is $19,300, and after 7 years, it's $13,700. This implies that in the span of 4 years (from year 3 to year 7), the car has lost $19,300 - $13,700 = $5,600 in value.

To find the yearly depreciation, we divide the total loss by the number of years. So, $5,600 ÷ 4 years = $1,400 per year. To find the initial value, we add the total depreciation after 3 years to the value after 3 years: $1,400 × 3 years = $4,200. Therefore the initial value is $19,300 + $4,200 = $23,500.

Marvin, on the other hand, needs to carefully assess beyond just price as similar mileage, exterior appearances, and age may not reveal the full story of the car's condition. Inspection reports, maintenance records, and potentially even fuel efficiency may impact the decision on which used car to buy.