Question

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?

Answer 1

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
`\bf \begin{cases} a+b=53500\implies \boxed{b}=53500-a\\\\ 0.10a+0.04b=4030\\ ----------\\ 0.10a+0.04\left( \boxed{53500-a} \right)=4030 \end{cases}`

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

what about "b"? well, b = 53500 - a