This website gave me the clues to solve the problem:

http://64.233.169.104/search?q=cache:mEUzlY9cinEJ:maven.smith.edu/~schicker/Lessons/purplemath/modules/investmt.htm+%22two+funds%22+%2B+invest+%2B+5%25+%2B+%22interest+income%22+%2B+algebra&hl=en&ct=clnk&cd=10&gl=us

The formula for finding simple interest is:

Interest = Principal * Rate

Let x = the amount invested at 5%

Now, let’s “plug and chug!”

$580 = .05x + .045($12,000 – x)

$580 = .05x + ($540 – .045x)

$580 = .05x + $540 – .045x

$580 = .005x + $540

.005x = $580 – $540

.005x = $40

x = $40 / .005

x = $8,000

So you invested $8,000 at 5% and $4,000 at 4.5% interest.

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* Always check your work *

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Interest = $8,000 * .05 = $400

Interest = $4,000 * .045 = $180

Interest = $400 + $180 = $580

Good luck in your studies,

~ Mitch ~