Brain Teasers
What is a Car Worth?
Henry is preparing to leave his parents' house, but before he goes, he needs a car and some money. His father agrees to give him $10,000 and a car if he works in the family store for a year. This sounds like a good deal to Henry, so he accepts.
After working for 7 months, Henry decides he has done enough. He quits his job, and his father says, "Fair enough. I will give you the car and $2,500."
Henry replies, "Knowing what the car is worth, that is perfectly fair."
What is the car worth?
After working for 7 months, Henry decides he has done enough. He quits his job, and his father says, "Fair enough. I will give you the car and $2,500."
Henry replies, "Knowing what the car is worth, that is perfectly fair."
What is the car worth?
Answer
The car is worth $8,000.If we denote the value of the car as 'c', then the value of 12 months of work would be 10000 + c, and the value of 7 months of work is 2500 + c.
Assuming that the value of a month of work is constant, we have the value of a month of work equaling (10000 + c)/(12 months) = (2500 + c)/(7 months). Since the two are equal, we can solve for c.
(7/12)*(10000 + c) = 2500 + c
(70000/12) - 2500 = c - (7/12)*c
3333.33 = (5/12)*c
8000 = c
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