SOLUTION: Should you consider fuel efficiency, measured in miles per gallon, when buying a new car? Suppose that car A costs $16,000 and gets 25 mi/gal, whereas car B costs $26,000 but gets

Algebra ->  Probability-and-statistics -> SOLUTION: Should you consider fuel efficiency, measured in miles per gallon, when buying a new car? Suppose that car A costs $16,000 and gets 25 mi/gal, whereas car B costs $26,000 but gets       Log On


   

Question 1201876: Should you consider fuel efficiency, measured in miles per gallon, when buying a new car? Suppose that car A costs $16,000 and gets 25 mi/gal, whereas car B costs $26,000 but gets 35 mi/gal. Further, assume that the price of gasoline is $4/gal and that you plan to drive the car for (m) mi. Taking into account price and fuel efficiency only,
(a) Write an expression CA for the cost of car A.

(b) Write an expression CB for the cost of car B.

(c) How many total miles m would you have to drive so that the cost is the same for both cars?

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Thank you!
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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Should you consider fuel efficiency, measured in miles per gallon, when buying a new car?
Suppose that car A costs $16,000 and gets 25 mi/gal, whereas car B costs $26,000 but gets 35 mi/gal.
Further, assume that the price of gasoline is $4/gal and that you plan to drive the car for (m) mi.
Taking into account price and fuel efficiency only,
(a) Write an expression CA for the cost of car A.
(b) Write an expression CB for the cost of car B.
(c) How many total miles m would you have to drive so that the cost is the same for both cars?
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(a)  CA = 16000 + 4%2A%28m%2F25%29  dollars.    (Notice that  m%2F25  is the number of gallons of fuel in this case,
                                               and  4%2A%28m%2F25%29  represents the cost of fuel for m miles)


(b)  CB = 26000 + 4%2A%28m%2F35%29  dollars.    (Notice that  m%2F35  is the number of gallons of fuel in this case
                                               and  4%2A%28m%2F35%29  represents the cost of fuel for m miles)


(c)  CA = CB  when

          16000 + 4%2A%28m%2F25%29 = 26000 + 4%2A%28m%2F35%29.


     To find m from this equation, simplify it step by step

          4%2A%28m%2F25%29 - 4%2A%28m%2F35%29 = 26000 - 16000

          m%2F25 - m%2F35 = 10000/4 = 2500

          35m - 25m = 2500*25*35

              10m   =  2187500

               m    =  218750 miles.    ANSWER

Solved.