Solution: Let the purchase price of A and B souvenirs be X yuan and Y yuan respectively, and get the equations.

① 7x+8y=380

② 10x+6y=380

Substitute the deformed y=(380-7x)/8 from ① into ②;

10x+6{(380-7x)/8 }=380

The solution is x=20.

Substitute x=20 into ① to get y=30.

A: The purchase prices of souvenirs A and B are 20 yuan and 30 yuan respectively.

(2) Solution: If X souvenirs A are purchased, then souvenir B is a 40-x inequality group:

① 20x+30(40-x)≤900

② 5x+7(40-x) ≥2 16

Solution: 30≤x≤32

So x can be 30,365,438+0,32.

When x=30, the profit is 220 yuan.

When x=3 1, the profit is 2 18 yuan.

When x=32, the profit is 2 16 yuan.

So x takes 30 hours or the most profit.

So when x=30, y= 10.

So we should buy 30 A-class souvenirs and 10 B-class souvenirs. Now we can get the biggest profit and the biggest value is 220 yuan.