Question

a man invested one third of his money at 5%, half of his money st 5.5%. if his total annual investment income was 735,how much had he invested?

Answer 1

Remark
Let the amount invest = x 

(1/3 x) * 5/100 + (1/2 x) * 5.5/100 = 735  Multiply numerators and denominators together on each side of the plus sign.

5x/300 + 5.5x / 200 = 735

Multiply both sides of the equation by 600 to get rid of the denominators.
(5x/300)*600 + (5.5x/200)*600 = 735 * 600
(5x * 2) + 5.5x * 3 = 441000  
10x + 16.5x = 441000   Combine the like terms on the left.
26.5 * x = 441000          Divide by 26.5 on both sides.
x = 441000/26.5
x = 16641.51 = invested amount <<<<< answer

Check
1/3 * 5/100 * 16641.51 = 277.36
1/2 * 5.5/100*16641.51 = 457.63
The total = 735 which is what it should be.