Solution: First, according to the meaning of the problem, make sure that you can't choose a 3 kg shopping bag, because if you choose a 3 kg shopping bag, the remaining 17 kg can't fit in any two shopping bags. So you can only choose from 5 kg and 8 kg shopping bags.

Suppose you choose x 5 kg shopping bags, and you need (3-X) 8 kg shopping bags. The meaning of the problems listed in this inequality is:

5X+8(3-X) ≧20, X≦4/3, where x is an integer and can only be 1 or 0, that is, they have two choices: (1) 1 and two 8kg ones, which need to be paid to the supermarket: 2+. (2) Three 8kg ones, which need to be paid to the supermarket: 3x3=9 yuan.

To sum up, they should at least pay the supermarket 8 yuan.