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According to the meaning of the question, if the cost of commodity A is X and the cost of commodity B is 2000-X,

And a linear equation is obtained: [1.3x+1.2× (2000-x) ]× 0.9-2000 = 277.

The equation is as follows: 1. Add 2000 to both sides and divide by 0.9 to get1.3x+1.2 (2000-x) = 2530.

2. Remove the brackets and combine similar items to get 0. 1X= 130.

Thus X= 1300 is obtained, and 2000-X=700 is deduced.

Therefore, the cost of commodity A is 1300 yuan, and the cost of commodity B is 700 yuan.