Percebt mixture problem

Question

I'm having trouble setting up the equation for and solving this problem:

Two factory plants are making tv panels. Yesterday Plant A produced 2000 fewer panels than Plant B did. 4% of the panels from Plant A and 5% from B were defective. How many panels did Plant A produce, if the two plants together produced 820 defective panels?

Answer 1

.04A + .05B = 820

A= B-2000

.04(B-2000) +.05B = 820

.04B +.05B = 820 + 80 = 900

B= 900/.09 = 100/.01 = 10,000

A = B-2000 = 8,000

.04(8,000) +.05(10,000) = 820