For each one-year period after a car was purchased, its value at the end of the year was 15% less than its value at the beginning of the year. If the value of the car 2 years after it was bought is $17,918, what was the value of the car when it was purchased?
Let's call the value of the car when it was purchased "x".
After one year, the value of the car is 15% less than x, or 0.85x.
After two years, the value of the car is 15% less than 0.85x, or 0.7225x.
We know that 0.7225x = $17,918. To solve for x, we can divide both sides by 0.7225:
x = $24,750
Therefore, the value of the car when it was purchased was $24,750.
Let's denote the value of the car when it was purchased as V.
After the first year, the value of the car would be given by V - 0.15V = 0.85V.
After the second year, the value of the car would be given by 0.85V - 0.15(0.85V) = 0.85V - 0.1275V = 0.7225V.
According to the given information, the value of the car 2 years after it was bought is $17,918, so we have:
0.7225V = $17,918
To find the value of the car when it was purchased (V), we divide both sides of the equation by 0.7225:
V = $17,918 / 0.7225
Calculating the value of V:
V ≈ $24,793.10
Therefore, the value of the car when it was purchased was approximately $24,793.10.