Final answer:
Ben invested $1,000 in the account earning 8% interest and $9,000 in the account earning 10% interest to have a total interest of $900 after one year.
Step-by-step explanation:
Let's suppose Ben invested $x in the account that earns 8% annual interest and $y in the account that earns 10% annual interest. The total amount invested is $10,000, so we have the equation x + y = 10000. The interest earned after one year is $900, so we can set up the equation 0.08x + 0.1y = 900.
Using these two equations, we can solve for x and y. To do this, we can multiply the first equation by -0.1 and add it to the second equation to eliminate y.
-0.1(x + y) + 0.1y = -0.1(10000) + 0.1y
-0.1x - 0.1y + 0.1y = -1000 + 0.1y
-0.1x = -1000
Dividing both sides by -0.1 gives x = 1000. Substituting this value back into the first equation, we find y = 9000.
Ben invested $1,000 in the account earning 8% interest and $9,000 in the account earning 10% interest.