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 purchased is $17,918, what was the value of the car when it was purchased?
Let's call the original value of the car "x".
After the first year, the car is worth 85% of its original value, or 0.85x.
After the second year, the car is worth 85% of its value after the first year, which is 0.85(0.85x) = 0.7225x.
We know that after two years, the car is worth $17,918:
0.7225x = $17,918
Solving for x:
x = $24,755
Therefore, the value of the car when it was purchased was $24,755.
Let's assume that the value of the car when it was purchased is "x".
After one year, the value of the car would be 85% of its original value:
Value after 1 year = x - 0.15x = 0.85x
After two years, the value of the car would be 85% of the value after one year:
Value after 2 years = 0.85(0.85x) = 0.7225x
Given that the value of the car after 2 years is $17,918, we can set up the equation:
0.7225x = 17,918
Solving for x, divide both sides of the equation by 0.7225:
x = 17,918 / 0.7225
x ≈ $24,793.76
Therefore, the value of the car when it was purchased was approximately $24,793.76.