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6%
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On the same day, Devin bought a car for $40,000 that would then decrease in value by $1200 per year, and Anita purchased a piece of real estate for $6,000 that would then increase in value by $500 per year. After how many years will Anita’s land be worth as much as Devin’s car?
A. 17
B. 18
C. 19
D. 20
E. 21
A. 17
B. 18
C. 19
D. 20
E. 21
08 Feb 2022, 07:43
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Bunuel
On the same day, Devin bought a car for $40,000 that would then decrease in value by $1200 per year, and Anita purchased a piece of real estate for $6,000 that would then increase in value by $500 per year. After how many years will Anita’s land be worth as much as Devin’s car?
A. 17
B. 18
C. 19
D. 20
E. 21
A. 17
B. 18
C. 19
D. 20
E. 21
The values of Devin's car are: 40000, 38800, 37600, .. and so on
The values of Anita's real estate are: 6000, 6500, 7000, .. and so on
Let the prices be equal after t years
Price of Devin's car = 40000 - 1200t
Price of Anita's real estate = 6000 + 500t
Since they are equal: 40000 - 1200t = 6000 + 500t
=> 1700t = 34000
=> t = 20 years
Answer D
Alternative:
The value of Devin's car = 40000
The value of Anita's real estate = 6000
Difference in price = 34000
Every year, Devin's car decreases by 1200 and Anita's real estate increases by 500
Thus, every year, the gap between the prices decreases by 1200 + 500 = 1700
Thus, time needed to have the gap of 34000 reduce to zero = 34000/1700 = 20 years
Note: We used the same idea as in relative speed
Answer D
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