Question

$9500 is invested, part of it at 12% and part of it at 9%. For a certain year, the total yield is $1032.00. How much was invested at each rate?

Answer 1

Let's say the amounts were "a" and "b", at 12% and 9% respectively

so... the total amount of those two, is $9500, since that was the total
amount invested, thus
a + b = 9500

now, 12% of a plus 9% of b, yielded $1032
12% of a is 12/100 * a or 0.12a
9% of b is 9/100 * b or 0.09b

thus

0.12a + 0.09b = 1032

$\bf \begin{cases} a+b=9500\to b=\boxed{9500-a}\\ 0.12a + 0.09b = 1032\\ --------------\\ thus \\\\ 0.12a + 0.09(\boxed{9500-a}) = 1032 \end{cases}$

solve for "a", to see how much was invested at 12%,

what about "b"? well, b = 9,500 - a