Question 420027: John is in the market for a new car and he’s narrowed his choices down to two: the Toyota Prius and the Hyundai Elantra. The Prius is advertised at $25,000 and gets 50 miles to the gallon. The Elantra is advertised at $15,000 and gets 30 miles to the gallon.
a) Assume John keeps the car for one year, gas costs a constant $3.00 a gallon, and that he could sell the Prius for $20,000 and the Elantra for $11,000. How many miles must John drive in order to justify purchasing the Prius?
b) Suppose you take into account that your bank is currently offering a one-year Certificate of Deposit that pays 5%. Now how many miles must he drive to justify purchasing the Prius?
My answer for a) is:
(250000-20000) + (n/50)*3 = (15000-11000) + (n/30)*3
--> n=25000 ( assume n is the miles need to drive in order to...)
I am not sure the following answer b) if correct
b)??
(250000-20000) + (n/50)*3 + 10000*.05 = (15000-11000) + (n/30)*3
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! John is in the market for a new car and he’s narrowed his choices down to two: the Toyota Prius and the Hyundai Elantra.
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The Prius is advertised at $25,000 and gets 50 miles to the gallon.
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The Elantra is advertised at $15,000 and gets 30 miles to the gallon.
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a) Assume John keeps the car for one year, gas costs a constant $3.00 a gallon, and that he could sell the Prius for $20,000 and the Elantra for $11,000. How many miles must John drive in order to justify purchasing the Prius?
Prius cost: P(x) = (25000-20000)+3(x/50) where x is the # of miles driven
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Elantra cost: E(x) = (15000-11000)+3(x/30)
Solve P(x) < E(x)
5000+3x/50 < 4000+x/10
1000 < 0.04x
x > 25,000 miles
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b) Suppose you take into account that your bank is currently offering a one-year Certificate of Deposit that pays 5%. Now how many miles must he drive to justify purchasing the Prius?
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P(x) = 5000 + (3x/50) + 0.05(25000)
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E(x) = 4000 + x/10 + 0.05(15000)
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Solve P(x) < E(x)
5000 + (3x/50) + 1250 < 4000 + (x/10) + 750
1000+ 500 < 0.04x
x > 37500 miles
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Cheers,
Stan H.
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