The weather suddenly turned cold.

(1) The number of C brand down jackets is 500-x-y (or 47-45x-110y);

(2) From the meaning of the problem:

400 x+550y+500(500 x-y)= 235000

Finishing: y = 2x-300；;

(3)①P =(500-400)x+(800-550)y+(650-500)(500-x-y)-2000，

And y = 2x-300,

∴ Sorting: P= 150x+43000

② The quantity of C brand down jackets purchased is:

500 x-y = 500 x-(2x-300)= 800-3x

According to the meaning of the problem, list the inequality groups.

x≥ 1002x？ 300≥ 100800? 3x≥ 100，

Solution: 200≤x≤7003

The range of ∴x is 200≤x≤x7003,

X is an integer, and the maximum value of X is 233.

∫ in P= 150x+43000, k = 150 > 0,

∴P increases with the increase of X.

When the maximum value of x is 233, the maximum value of p is 77950 yuan.

At this time, 233 sets of A, B and C brand down jackets were purchased, which were 166 sets and10/set respectively.