SOLUTION: The current price of a litre of gasoline is $0.92 and is expected to increase at a rate of 12% every six months.The price of a litre of diesel is $0.80 and is expected to increase

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The current price of a litre of gasoline is $0.92 and is expected to increase at a rate of 12% every six months.The price of a litre of diesel is $0.80 and is expected to increase       Log On

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Question 130285: The current price of a litre of gasoline is $0.92 and is expected to increase at a rate of 12% every six months.The price of a litre of diesel is $0.80 and is expected to increase at a rate of 15% every 4 months. If these trends continue, after how many months will both fuels have the same price per litre?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x="months until same price"

92(1.12)^(x/6)=80(1.15)^(x/4) __ dividing by 80 __ 1.15(1.12)^(x/6)=(1.15)^(x/4)

taking log __ log(1.15)+(x/6)(log(1.12))=(x/4)(log(1.15))

subtracting (x/6)(log(1.12))__ log(1.15)=(x/4)(log(1.15))-(x/6)(log(1.12))

factoring __ log(1.15)=x[(log(1.15))/4-(log(1.12))/6]

dividing by [(log(1.15))/4-(log(1.12))/6] __ (log(1.15))/[(log(1.15))/4-(log(1.12))/6]=x