Question

Last year, Dante had $10,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account

that paid 8% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account?

Answer 1

a = amount invested at 7%

b = amount invested at 8%

we know that total that he invested was 10000, therefore a + b = 10000.

hmmm how muich is 7% of "a"? well (7/100) * a => 0.07a.

how much is 8% of "b"? well (8/100) * b => 0.08b.

After a year he received in interest $730, so we know that at simple interest rate, 0.07a + 0.08b = 730.

`\begin{cases} a+b=10000\\ 0.07a+0.08b=730\\[-0.5em] \hrulefill\\ b = 10000 - a \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{0.07a+0.08(10000-a) = 730} \\\\\\ 0.07a+800-0.08a=730\implies 0.07a-0.08a=-70\implies -0.01a=-70 \\\\\\ a=\cfrac{-70}{-0.01}\implies \boxed{a = 7000} ~\hfill \stackrel{\textit{we know that}}{b = 10000 -a}\implies \boxed{b = 3000}`