(12 pts) Suppose the cost of driving an automobile is a linear function of the n
ID: 3018155 • Letter: #
Question
(12 pts) Suppose the cost of driving an automobile is a linear function of the number x of miles driven and that gasoline costs $3 per gallon. A certain automobile presently gets 20 mile per gallon, and a tune-up that will improve gasoline mileage by 10% costs $120. a. b. c. d. What is the mileage (mile per gallon) of the car after a tune-up? Express the cost of driving without a tune-up in terms of x. Express the cost of driving with a tune-up in terms of x. How many miles must the automobile be driven after a tune-up to make the cost of the tune-up worthwhile?Explanation / Answer
a)mileage of the car after a tuneup=20*(1+10%) =20*(1+(10/100)) =20*(1+0.1)=20*1.1=22
mileage of the car after a tuneup is 22 miles per gallon
b)
cost of driving without tuneup=x miles*(1/20)gallon/mile*3 dollars/gallon
cost of driving without tuneup=(3x/20) dollars
c)
cost of driving with tuneup=[x miles*(1/22)gallon/mile*3 dollars/gallon]+120 dollars
cost of driving with tuneup=(3x/22)+120 dollars
d)
(3x/20) =(3x/22)+120
=>(3x/20) -(3x/22)=120
=>3x(22-20)/(20*22)) =120
=>x =120*20*22/(3(22-20))
=>x =8800
automobile must be driven 8800 miles after a tuneup to make the cost of the tuneup worthwhile
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