Dave Horn invested half of his money at 5%, one-third of his money at 4%, and the rest at 3.5%. If his total annual investment income is $530, how much had he invested? Please list steps,
I have been stuck on this problem for hours, and other solutions for this problem do not make since.. Here's where I tried and failed:

.5*0.05 + .333*0.04 + (rest) .167* 0.035 or .5*5 + .333*4 + (rest) .167* 3.5 How is the answer $12,000?

Question

Dave Horn invested half of his money at 5%, one-third of his money at 4%, and the rest at 3.5%. If his total annual investment income is $530, how much had he invested? Please list steps, 
I have been stuck on this problem for hours, and other solutions for this problem do not make since.. Here's where I tried and failed:

.5*0.05 + .333*0.04 + (rest) .167* 0.035 or .5*5 + .333*4 + (rest) .167* 3.5 How is the answer $12,000?