Dave Horn, how much had he invested?

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?

Answer 1

Let the total investment is x 

Income from Half of the amount  at rate 5%  = 

Income from One third of  the amount  at rate 4% =

Remaining amount is = total amount - ( Half of the amoun + One third of  the amount)

= x - ( x/2 + x/3 )

= x - 5x/6

= x/6

Income from remaining amount at rate 3.5% = 

Total investment income is = 

Given investment income is $530

Dave Horn invested $12000