SOLUTION: Please help, ive been stuck on this question for the last 45 mins. QUESTION: A man invested half of his money at 5%, one-third of his money at 4%, and the rest of his money at

Question 901861: Please help, ive been stuck on this question for the last 45 mins.
QUESTION: A man invested half of his money at 5%, one-third of his money at 4%, and the rest of his money at 4.5%. If his total annual investment income was $550, how much had he invested?
What i got so far:
x/2(.05)+x/3(.04)+( i dont know what would go here)(.045)=$550
Thank you so much for your help in advance!!
Found 2 solutions by ewatrrr, lwsshak3:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
1 - 1/2 - 1/3 = 1 - 3/6 - 2/6 = 1/6
x/2(.05)+x/3(.04)+ x/6(.045)=$550 |Multiply thru by 6 so as all denominators = 1
3x(.05)+ 2x(.04)+ x(.045)=$550*6
x(.15 + .08 + .045) = $550*6
x = $550*6/.275

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A man invested half of his money at 5%, one-third of his money at 4%, and the rest of his money at 4.5%. If his total annual investment income was $550, how much had he invested?
***
let x=total amount invested
x/2=amt invested at 5%
x/3=amt invested at 4%
x-(x/2+x/3)=x-3x/6-2x/6=x/6=remaining amt invested at 4.5%
..
5%(x/2)+4%(x/3)+4.5%(x/6)=550
lcd:6
.05*3x+.04*2x+.045*x=3300
.15x+.08x+.045x=3300
x=12000
how much had he invested? $12,000
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