We have the following system of equations, given the information on the problem:
[tex]\begin{gathered} x+y=32000 \\ 0.02x+0.14y=2980 \end{gathered}[/tex]where 'x' represents the money in the account with 2% annual interest and 'y' represents the money in the account with 14%.
We can solve for x the first equation to get the following:
[tex]x=32000-y[/tex]doing the susbtitution on the second equation using this expression, we get:
[tex]\begin{gathered} 0.02(32000-y)+0.14y=2980 \\ \Rightarrow640-0.02y+0.14y=2980 \\ \Rightarrow0.12y=2980-640=2340 \\ \Rightarrow y=\frac{2340}{0.12}=19500 \\ y=19500 \end{gathered}[/tex]now that we know the value of y, we can use it to find the value of x:
[tex]\begin{gathered} x=32000-19500=12500 \\ \Rightarrow x=12500 \end{gathered}[/tex]therefore $12500 was invested at 2% and $19500 was invested at 14%
