Final answer:
To find out the additional amount to be invested, use the concept of weighted averages. Solve the equation (460 + (x * 3.5/100)) / (10,000 + x) = 4/100 to find x.
Step-by-step explanation:
To find out how much additional money the Knox Valley investment club should invest at an annual simple interest rate of 3.5% in order to earn a total annual interest of 4.0%, we can use the concept of weighted averages.
Let's assume the additional amount to be invested is x. The interest earned from the original investment of $10,000 at 4.6% is 10,000 * 4.6/100 = $460. The interest earned from the additional investment of x dollars at 3.5% is x * 3.5/100.
According to the problem, the total annual interest earned should be 4% of the total investment. So, the equation becomes (460 + (x * 3.5/100)) / (10,000 + x) = 4/100. By solving this equation, we can find the value of x.