Teacher Liu needs 480 tiles of the same specification from a certain brand to decorate the kitchen. These tiles are available in the decorative materials shopping mall of Shi Sheng Trade City.

Set up the purchase of large package X and small package Y,

According to the meaning of the question, 50x+30y = 480.

Because both x and y are nonnegative integers, the solution of the equation is x = 0? Y = 16 or? X = 3y = 1 1 or X = 6y = 6 or X = 9y = 1.

When x=0 and y= 16, the paid fee is: 0×30+ 16×20=320 (yuan);

When x=3 and y= 1 1, the paid fee is: 3× 30+11× 20 = 310 (yuan);

When x=6 and y=6, the fees paid are: 6×30+6×20=300 yuan;

When x=9 and y= 1? Payment: 9×30+ 1×20=290 yuan.

Therefore, it costs the least to buy 9 packages in large package and 1 package in small package, which costs 290 yuan.