Answer :
To solve this question we have to set and solve a system of equations.
Let S be the amount (in dollars) that Larry Mitchell invested in the 7% account, and T be the amount (in dollars) that he invested in the 2% account, then we can set the following system of equations:
[tex]\begin{gathered} S+T=16000, \\ 0.07S+0.02T=920. \end{gathered}[/tex]Solving the first equation for T we get:
[tex]T=16000-S\text{.}[/tex]Substituting T=16000-S in the second equation we get:
[tex]0.07S+0.02(16000-S)=920.[/tex]Applying the distributive property we get:
[tex]0.07S+320-0.02S=920.[/tex]Adding like terms we get:
[tex]0.05S+320=920.[/tex]Subtracting 320 from the above equation we get:
[tex]\begin{gathered} 0.05S+320-320=920-320, \\ 0.05S=600. \end{gathered}[/tex]Now, dividing by 0.05 we get:
[tex]\begin{gathered} \frac{0.05S}{0.05}=\frac{600}{0.05}, \\ S=12000. \end{gathered}[/tex]Finally, substituting S=12000 in T=16000-S we get:
[tex]\begin{gathered} T=16000-12000, \\ T=4000. \end{gathered}[/tex]Therefore, Larry invested $12,000 in the 7% account and $4,000 in the 2% account.
Answer: Larry invested $12,000 in the 7% account and $4,000 in the 2% account.