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Math problem (expert solution) award 20.
1. Buy a pair of shoes 180 yuan and get 4 pairs of socks 180 yuan; If you buy shoes at 180 yuan and add 4 pairs of socks * * * 5×4=20 yuan, if you pay 90%, it will be (180+5×4)×90%= 180 yuan. It can be seen that when buying socks is a multiple of 4, the cost of both is the same. If it is not a multiple of 4, the second case costs less.

If you want to buy 50 pairs of socks, because 50 is not a multiple of 4, you should choose the second option. Scheme 1 needs to buy 50÷4= 12.5, that is, 13 pairs of shoes and send 52 pairs of socks. The extra 2 pairs of socks are invalid, * * * cost180x13 = 2340 yuan; However, if the second scheme is adopted to directly purchase 13 pairs of shoes and 50 pairs of socks, * * will cost (13×180+5× 50 )× 0.9 = 2590× 0.9 = 2331yuan.

If you are restricted from buying 10 pairs of shoes and 50 pairs of socks, you should also choose the second scheme, which will cost (10×180+5× 50 )× 0.9 =1845 yuan.