Let x be the money Peter has invested in the 9% rate account, and y be the money in the 11% account, then we can set the following system of equations:
[tex]\begin{gathered} y=x+400, \\ 0.09x+0.11y=117. \end{gathered}[/tex]Substituting the first equation in the second one we get:
[tex]0.09x+0.11(x+400)=117.[/tex]Solving for x we get:
[tex]\begin{gathered} 0.09x+0.11x+44=117, \\ 0.2x=117-44=73, \\ x=\frac{73}{0.2}, \\ x=365. \end{gathered}[/tex]Substituting x=365 in the first equation we get:
[tex]y=365+400=765.[/tex]Answer: Peter has $365 invested in the 9% account and $765 in the other one.
