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During the period of 6 months, the price of gasoline increased 27%. Then, for the following 6 months, the price has decreased by 18%. By how much has the price

During the period of 6 months, the price of gasoline increased 27%. Then, for the following 6 months, the price has decreased by 18%. By how much has the price of gasoline change over this 12 months period?
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1 Answer

There are 2 price changes; the initial price (callit x0) falls to x1, then x1 rises to x2.
 
Part 1:  x0 falls by 27% to x1, this is the same as saying x1 = (1-.27)*x0 = 0.73*x0
          [ You can check this by the definition of fractional change :  (x1-x0)/x0  = -27 and solve for x1 ]
 
Part 2:  x1 rises by 18% to x2, this is the same as saying x2 = (1+.18)*x1 = 1.18*x1
 
Combining:   x1 = 0.73*x0,   x2=1.18*x1,   you get x2=1.18*(0.73*x0)  or x2 = 0.861*x0
 
The final price is only about 86% of the original, for a net decrease of 14%