Let P be the principal.
SI from the first account = [tex]\frac{PNR}{100}[/tex]
[tex]=\frac{x(1)(6)}{100}[/tex]
[tex]=\frac{6x}{100}[/tex]
SI from the second account = [tex]\frac{(x+405)(1)(5)}{100}[/tex]
[tex]=\frac{5(x+405)}{100}[/tex]
Total money earned in interest after 1 year = $204.
Therefore, [tex]\frac{6x}{100} +\frac{5(x+405)}{100} =204[/tex]
[tex]\frac{6x+5x+2025}{100} = 204[/tex]
[tex]\frac{11x+2025}{100} =204[/tex]
11x + 2025 = 20400
11x = 20400 - 2025
11x = 18375
x = 18375/11
x = 1670.45
x + 405 = 1670.45 + 405 = 2075.45
Hence, Barneys investment in the first account is $1670.45 and her investment in the second account is $2075.45.
