Question

In planning her​ retirement, Liza deposits some money at 3.5​% ​interest, with twice as much deposited at 4.5​%. Find the amount deposited at each rate if the total annual interest income is ​$2250.

Answer 1

a = amount deposited at 3.5%

b = amount deposited at 4.5%

we know that "b" is twice as much as "a", thus b = 2a.

`\begin{array}ll \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{3.5\% of a}}{\left( \cfrac{3.5}{100} \right)a}\implies 0.035a \\\\[-0.35em] ~\dotfill\\\\ \begin{array} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4.5\% of 2a}}{\left( \cfrac{4.5}{100} \right)2a}\implies 0.045(2a)`

we also know that whatever "a" amount is, their sum is 2250, thus

`0.035a+0.045(2a) = 2250\implies 0.035a+0.09a=2250\implies 0.125a=2250 \\\\\\ a=\cfrac{2250}{0.125}\implies \boxed{a=18000}~\hspace{10em}\boxed{\stackrel{2a}{b=36000}}`