Question

Mr. Wilson invested money in two accounts. His total investment was $20,000. If one account pays 5% in interest and the other pays 2% in interest, how much does he have in each account if he earned a total of $550 in interest in 1 year?

Answer 1

a = amount invested at 5%

b = amount invested at 2%

now, we know the total invested by Mr Wilson was 20000, so whatever "a" and "b" might be, we know that a + b = 20000.

$a + b = 20000\implies b = 20000-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{5\% of a}}{\left( \cfrac{5}{100} \right)a}\implies 0.05a~\hfill \stackrel{\textit{2\% of b}}{\left( \cfrac{2}{100} \right)a}\implies \begin{array}{llll} 0.02b\\\\ \stackrel{substituting}{0.02(20000-a)} \end{array}$

now, we know the total of earned interest is 550 bucks, so then

$0.05a~~ + ~~0.02(20000-a)~~ = ~~550\implies 0.05a+400-0.02a=550 \\\\\\ 0.03a+400=550\implies 0.03a=150\implies a=\cfrac{150}{0.03}\implies a=5000 \\\\\\ ~\hspace{24em}\stackrel{20000~~ - ~~5000}{b=15000}$