Final answer:
To solve this problem, set up a system of equations. The solution is $2500 invested at 10% and $6500 invested at 12%.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let x be the amount invested at 10% and y be the amount invested at 12%. The total amount invested is $9000, so we have the equation x + y = 9000.
The total interest earned after one year is $1030. The amount invested at 10% will earn 10% interest, or 0.10x, and the amount invested at 12% will earn 12% interest, or 0.12y. So we have the equation 0.10x + 0.12y = 1030.
We can solve this system of equations to find the values of x and y. Multiplying the first equation by 0.10, we get 0.10x + 0.10y = 900. Subtracting this equation from the second equation, we get 0.02y = 130. Solving for y, we find that y = 6500. Substituting this value back into the first equation, we can solve for x. x + 6500 = 9000, so x = 2500.
Therefore, $2500 was invested at 10% and $6500 was invested at 12%.