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?
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%