Respuesta :
a = amount invested at 9%
b = amount invested at 11%
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hfill \stackrel{\textit{9\% of "a"}}{\left( \cfrac{9}{100} \right)a\implies 0.09a}~\hfill \stackrel{\textit{11\% of "b"}}{\left( \cfrac{11}{100} \right)b\implies 0.11b}[/tex]
we know she has a total of $40,000 to invest, so, if she invested "a" amount in one, the other quantity must be the slack left from 40,000 and "a", namely b = 40000 - a.
we also know that the yield or earned interest from both amounts is 4300, thus
[tex]\bf \stackrel{\textit{yield of "a"}}{0.09a}~~+~~\stackrel{\textit{yield of "b"}}{0.11b}~~=~~\stackrel{\textit{annual income from both}}{4300} \\\\\\ \stackrel{\textit{yield of "a"}}{0.09a}~~+~~\stackrel{\textit{yield of "b"}}{0.11(40000-a)}~~=~~4300 \\\\\\ 0.09a+4400-0.11a = 4300\implies -0.02a+4400 = 4300 \\\\\\ 4400=4300+0.02a\implies 100=0.02a\implies \cfrac{100}{0.02}=a\implies \boxed{5000=a} \\\\\\ \stackrel{\textit{we know that}}{b = 40000-a}\implies \boxed{b = 35000}[/tex]
