Dave Horn invested half of his money at 5%, one-third of his money at 4%, and the rest of his money at 3.5%. If his total annual investment income was $530, how much had he invested.

return = 0.5(0.05) + 0.3333(0.04) + ( 1 - 0.50 - 0.3333)(0.035)

= 0.025 + 0.01333 + 0.00583

= 0.04417

$530 / 0.04417 = $12,000

if x is amount invested, then (1/2)x * 0.05 + (1/3)x * 0.04 + (1/6)x * 0.035 = 530.

solve for x