Final answer:
To solve the problem, let x be the amount invested at 8% and y be the amount invested at 12%. Use the given equations to solve for x and y. $2,500 is invested at 8% and $3,500 is invested at 12%.
Step-by-step explanation:
To solve this problem, let x be the amount invested at 8% and y be the amount invested at 12%. We know that the total amount invested is $6,000, so we have the equation x + y = 6000. We also know that the annual interest earned is $620, which can be expressed as 0.08x + 0.12y = 620.
To solve this system of equations, we can use substitution or elimination. Let's use substitution by solving the first equation for x: x = 6000 - y. Substituting this expression for x in the second equation, we have 0.08(6000 - y) + 0.12y = 620. Simplifying, we get 480 - 0.08y + 0.12y = 620. Combining like terms, we have 0.04y = 140. Dividing both sides by 0.04, we find that y = 3500. Substituting this value back into the first equation, we find that x = 2500.
Therefore, $2,500 is invested at 8% and $3,500 is invested at 12%.