Two investments totaling $53,500$⁢53,500 produce an annual income of $4030$⁢4030. one investment yields 10%10% per year, while the other yields 4%4% per year. how much is invested at each rate?

Let's say the amounts invested are "a" and "b", at 10% and 4% respectively

so, we know the total investment was 53,500, thus their sum is just that much
a + b = 53500

and we also know, they yield an income of 4,030
now, how much is 10% of a? well 10/100 * a or 0.10a

how much is 4% of b? well, 4/100 * b or 0.04b

we know their yield is 4,030, thus  0.10a + 0.04b = 4030

thus  

solve for "a", to see how much was invested at 10%

what about "b"?  well, b = 53500 - a

55, 90 and 35 (when you add it, it should be 180)