Katie invested a total of $8000, part at 5% simple interest and part at 6% simple interest. at the end of 1 year, the investments had earned $455 interest. how much was invested at each rate?

She invested "a" at 5% and "b" at 6%.

now, we know whatever amounts "a" and "b" are, they add up to 8000, thus a + b = 8000.

how much is 5% of a? well, (5/100) * a, or 0.05a.
how much is 6% of b? well, (6/100) * b, or 0.06b.

After a year, their combined interest, their yield, was 455, thus, we also know that 0.05a + 0.06b = 455.



how much was invested at 6%?  well, b = 8000 - a.