Question

Roberto invested some money at 5%, and then invested $2000 more than twice this amount at 5%. His total annual income from the two investments was $2200. How much was invested at 5%?

Answer 1

Roberto initially invested $14000 at 5%. This was determined by setting up an equation with the initial investment as x, and using the given total annual income to solve for x.

Step-by-step explanation:

We need to solve for the initial amount Roberto invested at 5% before investing the additional amount. Let's call the initial investment x. According to the problem, Roberto then invests $2000 more than twice this amount at the same rate. Thus, the second investment amount would be 2x + $2000. The total income from both investments is $2200, and both investments earn 5% per year. So, we can set up the equation as: 0.05x + 0.05(2x + 2000) = 2200. Simplifying this equation, we have 0.05x + 0.1x + 100 = 2200, which further simplifies to 0.15x = 2100. Dividing both sides by 0.15 gives us x = $14000. Therefore, Roberto initially invested $14000 at 5%.