Its a math question thats really simple but i need help explaining the steps if you wouldnt mind helping ?

Question

suppose you're considering trading in your car ( which gets 10 mpg)for one that gets 30 mpg, but it will cost you $5400 if you drive 240 miles per weeks how many weeks will it take fot the new car to "pay for its self"- save you $5400 in gas money assume that gas is $4 a gallon and that all other expenses for the two cars are the same.

Answer 1

amount of gas you now use / week

240/10 = 24 gallon

amonut of gas you will be using with the new car / week

240/30 = 8 gallon

potential saving 16 gallon/week and in money terms it is $64/week

Your investment is $5,400 and it will need 5400/64 weeks to break even, or 84.375 weeks (around 1 year 32 weeks and 3 days approx)

Hope this come to your help :))

Answer 2

x($4.00[240/{30 - 10}]) = $5,400.00

x($4.00[240/20]) = $5,400.00

x($4.00[12]) = $5,400.00

x($48.00) = $5,400.00

x = $5,400.00/$48.00

x = 225/2 or 112 1/2

Answer: 225/2 or 112 1/2 weeks

Proof (savings of $5,400.00 for 112 1/2 weeks):

= $4.00 per gallon(240 mi/[30 mpg - 20 mpg]) * 112 1/2 weeks

= $4.00 per gallon(240 mi/20 mpg) * 112 1/2 weeks

= $4.00 per gallon(12 gallons per week) * 112 1/2 weeks

= $48.00 savings per week * 225/2 weeks

= $10,800.00/2

= $5,400.00

Answer 3

every gallon you drive in the new car you will be earning/saving 20 miles free or two gallons on the old car, so

240/30=8 gallons 8x4=$32 per week

5400/32=168.75 weeks    

Answer 4

You are essentially getting 20 more miles per gallon with the new car.

If you drive 240 miles / week....

(240 mi / 1 wk) (1 gal / 20 mi) ($4 / gal) = $48 / week

$5400 (1 week / $48 ) = 112.5 weeks.  (ANSWER)

Or that would be a little over 2 years.

Hope that helps.

Answer 5

There appears to be a lot on info but it helps to break it down.

Old car: 240 miles at 10mpg with gas at $4/gallon every week.

Every 10 miles costs your car $4.

240 / 10 = 24 gallons

24 gallons * $4 per gallon = $96

New Car: 240 miles at 30mpg with gas at $4/gallon every week

Every 30 miles costs your car $4

240 / 30 = 8 gallons

8 gallons * $4 per gallon = $32

Every week you are saving 96 - 32 = $64

The new car costs $5400 divided by the saving per week $64 = number of weeks to 'pay for itself'

5400 / 64 = 84.375

Since it's difficult to tell when .375 of a week is through, it will take 85 weeks.

Answer 6

240/week at 10mpg is 24 gallons per week

240/week at 30mpg is  8 gallons per week so you're "saving" 16 gallons per week at $4/gallon you're saving 64/week

5400/64 = 84.375 weeks to break even