A man invested one fifth of his money at 4%, half of his money at 5%, and the rest of his money at 3.5%. If his total annual investment income was $870, how much had he invested?

The man invested 1/5 of the money at 4/100. Which says he earns 4/500 of his total money on one month.

He also invested 1/2 of the money at 5/100. Which means he earns 5/200 of his total money per month.

For the last part, he spent the rest of the money which is: x + 1/5 + 1/2 = 1

Make the denominators equal: x + 2/10 + 5/10 = 10/10

Add like terms: x + 7/10 = 10/10

Substract 7/10: x=3/10

He gave this money for 3.5/100 interest. Which equals 10.5/1000 of his total money.

When you add the three values: 4/500 + 5/200 + 10.5/1000

Make denominators equal: 8/1000 + 25/1000 + 10.5/1000

Add the like terms: 43.5/1000

This means the man's money's 43.5/1000 is equal to $870

Set the values equal: 43.5x/1000 = 870

Make the denominators equal: 43.5x/1000 = 870,000/1000

Multiply with 1000: 43.5x = 870,000

Divide both sides by 43.5: x = 20,000

The man's total money is $20,000