SOLUTION: My car gets 12 miles per gallon of gasolene. Gas is 4$/gallon. If I buy a car that gets 16 miles per gallon at a cost of $500, how long or how many miles will it take me to pay f

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Question 148235: My car gets 12 miles per gallon of gasolene. Gas is 4$/gallon.
If I buy a car that gets 16 miles per gallon at a cost of $500, how long or how many miles will it take me to pay for it with savings of gas cost?
Help please,
Bob

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
My car gets 12 miles per gallon of gasoline. Gas is 4$/gallon.
If I buy a car that gets 16 miles per gallon at a cost of $500, how long or how many miles will it take me to pay for it with savings of gas cost?
:
Let x = no. of miles to recover $500
:
Cost to drive old car: 4(x/12)
Cost to drive new car: 4(x/16)
:
Old car cost - new car cost = $500
%284x%29%2F12 - %284x%29%2F16 = 500
Cancel the 4's
x%2F3-x%2F4 = 500
Multiply equation by 12; gets rid of the denominator and you have
4x - 3x = 12(500)
;
x = 6000 mi to recover the $500 spent (Lose the $ sign)
:
:
Check solution:
4(6000/12) - 4(6000/16) =
2000 - 1500 = 500