Shops usually use the following methods to determine the price of mixing two kinds of candy. Let the unit price of candy A be C yuan/kg, and the price list of candy B be D yuan/kg. Then the unit price of candy mixed with candy A and candy B is mc+md/m+n yuan /kg. At present, two kinds of mixed sugars A and B are made by mixing two kinds of sugars with different unit prices. Among them, the mixed sugar A consists of 10 Jin A sugar and 10 Jin B sugar, and the mixed sugar B consists of 100 Yuan A sugar and 100 Yuan B sugar. What kind of mixed sugar do you think has a higher unit price? Why?

Solution, get:

The unit price of methyl sugar is (10a+10b)/20 = (a+b)/2.

The unit price of ethyl sugar is (100+100)/(100/a+100/b) = 2ab/(a+b).

Assuming that the unit price of A is not greater than B, there are:

(a+b)/2 & lt； =2ab/(a+b) because a, b >；; 0

So: (a+b) 2

a^2+2ab+b^2<； =4ab

a^2-2ab+b^2<； =0

(a+b)^2<； =0

The square of any number is not less than 0, and a, b >；; 0

So the above formula should be greater than 0, so the assumption is not valid.

The conclusion is that the unit price of A is greater than that of B.

A:A's unit price is relatively high.