Kevin invested $4,000 in an account which earns 6% interest per year and $x in a different account that earns 8% interest per year. How much is invested at 8% if the total amount of interest earned annually is $405.50?

Let x = the amount invested at 8% interest. Since the total interest is $405.50, use the equation 0.06(4,000) + 0.08x = 405.50. Simplify the multiplication: 240 + 0.08x = 405.50. Subtract 240 from both sides: 240 - 240 + 0.8x = 405.50 - 240; simplify: 0.08x = 165.50. Divide both sides by 0.08: 0.08x/0.08=165.50/0.08. Thus, x = $2,068.75, that is the amount invested at 8% interest.