Question

Larry invested part of his 17,000 advance at 5% annual simple interest and the rest at 3% annual simple interest. if his total yearly interest from both accounts was $530, find the amount invested at easch rate.

Answer 1

bearing in mind that
`\bf \begin{array}c \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}`

a = amount invested at 5%

b = amount invested at 3%

how much is 5% of "a"? well is simply (5/100) * a, or 0.05a.

how much is 3% of "b"? well is simply (3/100) * b or 0.03b.

we also know that "b" is the rest invested after "a" was invested, so since the total amount is 17000, then a + b = 17000, b = 17000 - a.

and since the yield or amount of both of those interests after the same year is 530, then

`\bf 0.05a+0.03b=\stackrel{yield}{530}\implies 0.05a+0.03(\stackrel{b}{17000-a})=530 \\\\\\ 0.05a-0.03a+510=530\implies 0.02a=20\implies a=\cfrac{20}{0.02} \\\\\\ \blacktriangleright a=1000 \blacktriangleleft ~\hspace{10em}b=17000-1000\implies \blacktriangleright b=16000\blacktriangleleft`