Question

Bernadette inherited 15000 and invested it in two municipal bonds , witch pay 7% and 9% simple interest. The annual interest is 1230. Find the amount at each rate.

Answer 1

let's say she invested "a" amount at 7% and "b" amount at 9%

we know, whatever "a" and "b" are, they add up to 15000, thus

a + b = 15000

how much is 7% of a? well, (7/100) * a, or 0.07a
how much is 9% of b? well, (9/100) * b, or 0.09b

we know the sum of the interest for both is 1230, thus

0.07a + 0.09b = 1230

thus
`\bf \begin{cases} a+b=15000\implies \boxed{b}=15000-a\\ 0.07a+0.09b=1230\\ ----------\\ 0.07a+0.09\left( \boxed{15000 - a} \right) = 1230 \end{cases}`

solve for "a", to see how much was invested at 7%

what about "b"? well, b = 15000 - a