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Suppose you drive an average of 12,000miles per​ year, and your car gets 25 miles per gallon. Suppose gasoline costs ​$ 2.60 a gallon.
a. How much money do you spend each year on​ gasoline?
b. You plan to trade in your car for one that gets x more miles per gallon. Write an expression to represent the new yearly cost of gasoline.
c. Write an expression to represent your total savings on gasoline per year.
d. Suppose you can save ​$400 a year with the new car. How many miles per gallon does the new car​ get?

Respuesta :

boatengalbert291
a) If 25 miles =1 gallon

Then 12000=12000/25=480 gallons

If 1 gallon =$2.6

Then 480 gallons = 480 x 2.6
= 1248.00

b) If (25 + x)miles =1 gallon

Then 12000miles=1200/(25+x)
gallons

c) (31200/(25+x)) - (1248/(25+x)

=(31200-1248(25+x)) / (25+x)

=1248((25- (25+x))/(25+x)

=1248x/(25+x)

d) 1248x/(25+x)=400. Cross
multiply

1248x =10000+400x. Group like
terms

848x/848=10000/848

x=11.79

=(25+x)=(25+11.79)

=36.79 miles per gallon

a)The cost of 480 gallons =  $1248

b)Expression to represent the new yearly cost of gasoline =  $ 31200/ (25+x)

c)total savings on gasoline per year =$1248x/ 25+ x

d)miles per gallon does the new car​ get = 36.79 miles

What is unitary method?

Unitary method Technique to solve a problem by first finding the value of a single unit , and then finding the necessary value by multiplying the single unit value.

Given :

drive an average of = 12000miles per year

one gallon consumed = after every  25 miles

cost per gallon of gasoline = $ 2.60

a)  25 miles consume = 1 gallon of gasoline

      12000 mile will consume = (1/ 25)* 12000 =480 gallons

     cost of one gallon = $ 2.60

     cost of 480 gallons = $ 2.60 * 480=  $1248

b) another car gives x more miles per gallon :

       25 + x miles consume = 1 gallon

       12000 miles will consume = 1/ (25+x) * 12000 gallons

       cost of one gallon = $ 2.60

       cost of 1/ (25+x) * 12000 gallons=  2.60 * (1/ (25+x) * 12000)

                                                            =  $ 31200/ 25+x

c)Total savings will be = cost  spent in initial case - cost in 2nd case

                                     =   1248 - 31200/(25+x)

                                     = (31200 + 1248 x - 31200)/ (25+x)

                                     = $1248x/ 25+ x        equation 1

d) let saving = $ 400  (given )     equation 2

    savings calculated in previous part =$1288x/ 25+ x

    equating both the equations 1 and 2

   1248x/ 25+x = 400

    1248x = 10000 + 400x

    1248x -400x = 10000

    x = 11 .79 miles

Total miles covered per gallon = 25 + x = 25 + 11.79 = 36.79 miles

learn more about unitary method :

https://brainly.com/question/14793162?referrer=searchResults

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