Question

A new car worth $25,000 is depreciating (loses value) in value by $1,250 per year. Determine how many years will it take for the car to be worth $8,500?

Answer 1

so, when the car is new is 25000.

after 1 year is 25000 - 1250

after 2 years is 25000 - 1250 - 1250, or just 25000 - 1250(2)

after 3 years is 25000 - 1250 - 1250 - 1250, or just 25000 - 1250(3)

after 4 years is 25000 - 1250(4)

after "x" years is 25000 - 1250x.

so, say the current price is hmmm "y", and "x" is years passed, thus

y = 25000 - 1250x.

we know that after "x" years, the car became worth only 8500, namely y = 8500, thus


`\bf \stackrel{y}{8500}=25000 - 1250x\implies 1250x+8500=25000 \\\\\\ 1250x=25000 - 8500\implies 1250x=16500\implies x=\cfrac{16500}{1250} \\\\\\ x=\cfrac{66}{5}\implies x=13(1)/(5)`

so pretty much after 13 years, 2 months, 7 days and 12 hours.