The hybrid version of an automobile costs $4000 more than the gasoline version of the same model of automobile. The hybrid version averages 42 miles per gallon of gasoline and the gasoline version averages 28 miles per gallon. Assuming that gasoline will cost $4 per gallon and that you will drive 14,000 miles per year, how many years will be required for you to make up the extra original purchase cost in savings on the cost of gasoline.

Question

The hybrid version of an automobile costs $4000 more than the gasoline version of the same model of automobile.  The hybrid version averages 42 miles per gallon of gasoline and the gasoline version averages 28 miles per gallon.  Assuming that gasoline will cost $4 per gallon and that you will drive 14,000 miles per year, how many years will be required for you to make up the extra original purchase cost in savings on the cost of gasoline.

BlackTom AI · Accepted Answer

Start by identifying the key numbers and what needs to be compared. The hybrid costs $4000 more upfront, while annual fuel costs differ due to fuel efficiency. 
Option 3: 3 years. Compute annual fuel usage and cost for both cars. Gasoline version uses 14,000 miles / 28 mpg = 500 gallons per year, costing 500 × $4 = $2000. Hybrid uses 14,000 / 42 = 333.33 gallons per year, costing 333.33 × $4 ≈ $1333.33. Annual savings from using the hybrid ≈ $2000 − $1333.33 = $666.67. If you break even in 3 years, you’d accumulate about 3 × 666.67 ≈ $2000, which is far short of the $4000 extra price, so 3 years cannot recoup the higher upfront cost. 
Option 1: 1 year. With the annual savings of about $666.67, you would recover only about $666 in the first year, far less than the $4000 premium, so 1 year is insufficient.
Option 12: 12 years. After 12 years, total savings would be 12 × 666.67 ≈ $8000, which would exceed the $4000 premium, so 12 years would certainly cover the extra cost, but the question asks for when you first break even, so this overestimates the needed time.
Option 6: 6 years. With yearly savings around $666.67, six years yield 6 × 666.67 ≈ $4000, which matches the additional purchase cost, indicating a break-even at six years precisely. 
Option 2: 2 years. Two years of savings amount to about 2 × 666.67 ≈ $1333.34, far below the $4000 premium, so this short time frame cannot recoup the extra cost. 
Putting the pieces together, the only interval that aligns with recouping a $4000 premium given the computed yearly savings is around six years, since 6 × 666.67 ≈ 4000. The other options either fall short of the premium or extend beyond the break-even point without hitting it exactly.}

MATH 1151 AU2025 (18443) Calculus Concept Readiness Assessment (CCR)

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