[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 2.3\%\to \frac{2.3}{100}\dotfill &0.023\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (5000)(0.023)(3)\implies I=345[/tex]
so then she grabs those 345 earned and puts it in the second account earning 3.2%, how long till that yields 55.20 bucks in interest alone?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$55.20\\ P=\textit{original amount deposited}\dotfill & \$345\\ r=rate\to 3.2\%\to \frac{3.2}{100}\dotfill &0.032\\ t=years \end{cases} \\\\\\ 55.20 = (345)(0.032)(t)\implies \cfrac{55.20}{(345)(0.032)}=t\implies 5=t[/tex]
