Aman 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? how can i set this up?

Namely the interest yield  is $870, so all those investments yielded that much after a year.

a = the whole amount he invested.

let's keep in mind that whatever% of anything is just (whatever/100) * anything.

now 1/5 of "a" went with 4%, how much is 1/5 of "a"? well is (1/5)a or a/5.

how much is 4% of a/5?  well is just (4/100) * (a/5) or 0.04a/5.

he invested 1/2 at 5%, namely (1/2)a or a/2, and 5% of that is just (5/100) (a/2) or 0.5a/2.

and the rest, hmmm what's the rest?  well, 1/2 taken up and then 1/5  taken up, so the rest is the difference of the full amount minus those hmmm let's see



and that was invested at 3.5%, what is 3.5% of that?  well is just (3.5/100) * (3a/10), or 0.105a/10.

we know the sum of all those yields was 870 bucks, thus