Analysis: The solution to this problem is to compare the average price of A and B to pump oil twice.

Solution: The oil price of this grain and oil store is X yuan per kilogram for the first time and Y yuan per kilogram for the second time.

A goes to pump one kilogram of oil every time, and B goes to pump oil for B yuan every time. According to the meaning of the question,

A The average price of two pumps is: (ax+ay) ÷ 2a = (x+y)/2.

B The average price of two trips to pump oil is:

Now compare the size of (x+y)/2 and 2xy/(x+y) as a commercial law.

That is (x+y) 2/4xy.

Because (x-y) 2 ≥ 0

So x 2+y 2 ≥ 2xy

Then (x+y) 2/4xy = x2+y2+2xy/4xy ≥ 2xy+2xy/4xy =1.

Therefore, the method of (x+y)/2≥2xy/(x+y), that is, A, is more economical.