Question

An executive invests $20,000, some at 9% and some at 10% annual interest. If he recieves an annual return of 1,980,how much is invested at each rate?

Answer 1

he invested "a" at 9% and "b" at 10%

now, we know he's investing 20,000, so whatever "a" and "b" are, they sum up to 20000

a + b = 20000

how much is 9% of a? well, (9/100) * a, or 0.09a
how much is 10% of b? well, (10/100) * b or 0.10b

we know, his annual interest returns are 1980 for both, so

0.09a + 0.1b = 1980


`\bf \begin{cases} a+b=20000\implies \boxed{b}=20000-a\\ 0.09a + 0.1b = 1980\\ ----------\\ 0.09a + 0.1\left( \boxed{20000-a}\right) = 1980 \end{cases}`

solve for "a", to see how much he invested at 9%

what about "b"? well, b = 20000 - a