(1-9) A family wishes to buy a new midsize automobile. The two options they cons
ID: 1818026 • Letter: #
Question
(1-9) A family wishes to buy a new midsize automobile. The two options they consider are (a) a standard automobile with an SI engine that gets 31 miles per gallon fuel economy (mpg) and costs $18,000; and (b) a hybrid automobile that gets 82 mpg and costs $32,000. On average, the family drives 16,000 miles per year, and gasoline costs $1.65 per gallon.Calculate:
(a) Amount of gasoline each vehicle would use each year.(gal)
(b) Gasoine cost savings of hybrid over standard.($/year)
(c) Time it would take to make up the difference in vehicle cost, with fuel savings. Disregard any interest on car loans and time-worth of money. (months)
Explanation / Answer
a) 16000 miles at 31mpg => 16000/31 = 516.13 gallon at 82mpg => 16000/82 = 195.12 gallon b) cost/year with standard car: 516.13*1.65$ = 815.61 $ hybrid car: 195.12*1.65$ = 312.95 $ => saving/year: 815.61-312.95 = 529.66$ c) => cost per month for gasoline: standard: 815.61/12 hybrid: 312.95/12 => Total costs: standard: (815.61/12)*X + 18000 hybrid: (312.95/12)*X + 32000 with X the number of months When are these equal? => (815.61/12)*X + 18000 = (312.95/12)*X + 32000 => {(815.61/12)-(312.95/12)}*X = 14000 => X = 334 or almost 28 years
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