Question

Mrs. Jackson has $7,000 to invest. If she invests part at 6% simple annual interest and part at 8% simple annual interest, she will get an annual return of $520. How much should she invest at 8%?

Answer 1

let's say she invest the amounts of "a" at 6% and "b" at 8%.

well, she has to invest on both amounts, 7000 total, thus a + b = 7000

how much is 6% of a? well, (6/100) * a, or 0.06a.
how much is 8% of b? well, (8/100) * b, or 0.08b.

now, we know the annual return in interest from those two amounts is 520.
thus 0.06a + 0.08b = 520

$\bf \begin{cases} a + b = 7000\implies \boxed{a} = 7000-b\\ 0.06a + 0.08b = 520\\ --------------\\ 0.06\left( \boxed{7000 - b} \right)+0.08b = 520 \end{cases}$

solve for "b".