Question

Trent invests $8700 in two different accounts. The first account paid 4 %, the second account paid 8 % in interest. At the end of the first year he had earned $540 in interest. How much was in each account

please i need it

Answer 1

a = amount invested at 4%

b = amount invested at 8%

we know the total amount invested is 8700, so if he invested "a" already, the second amount must be b = 8700 - a.

`\bf \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{4\% of a}}{\left( \cfrac{4}{100}\right)a\implies 0.04a}~\hfill \stackrel{\textit{8\% of b}}{\left( \cfrac{8}{100} \right)b\implies 0.08b} \\\\[-0.35em] ~\dotfill`

`\bf \stackrel{\textit{sum of the percentages}}{0.04a+0.08b}~~=~~\stackrel{\textit{yield for 1 year}}{540}\implies 0.04a+0.08\left(\boxed{8700-a} \right) = 540 \\\\\\ 0.04a-0.08a+696=540\implies -0.04a+696=540\implies -0.04a=-156 \\\\\\ a= \cfrac{-156}{-0.04}\implies \blacktriangleright a = 3900 \blacktriangleleft~\hfill b = 8700-3900\implies \blacktriangleright b = 4800 \blacktriangleleft`