[tex] \frac{a}{b} = \frac{2}{3} \\ \frac{a + 400}{b - 400} = \frac{4}{5} \\ a = \frac{2b}{3} \\ 5a + 2000 = 4b - 1600 \\ \frac{10b}{3} = 4b - 1600 \\ 1600 = \frac{12b}{3} - \frac{10b}{3} \\ \frac{2b}{3} = 1600 \\ 2b = 1600 \times 3 \\ 2b = 4800 \\ b = 2400 \\ a = \frac{4800}{3} = 1600[/tex]
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