$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?

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



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

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