Answer:
$37500
Step-by-step explanation:
A new car loses 20% of its original value when you buy it and 8% of its original value per year . A 6 year old car is worth $12000 what was the original value?
Solution:
Let V represent the original value of the car, and let D be the value of the car after y years.
Immediately the car is bought it has 20% of its initial value, and it loses 8% of its value per year. Hence:
At zero years, (y = 0); D = V - 20% of V = V - 0.2V = 0.8V (it loses 20%)
After y years: D = 0.8V - (8% of V)y = 0.8V - (0.08V)y
From the question, the car is worth $12000 after 6 years. y = 6, D = $12000, we are to find V:
D = 0.8V - (0.08V)y
Substituting:
12000 = 0.8V - (0.08V * 6)
12000 = 0.8V - 0.48V
12000 = 0.32V
V = 12000 / 0.32
V = 37500
V = $37500
