https://file.aiquickdraw.com/mathbot/file/1725512683939xezbgkao.jpg

Let's break down the problem from the image and solve it step by step.

**Problem:**
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%?

Let:
- $ x $ be the amount of money invested at 5%.

The second investment is $2000 more than twice the first investment, so the second investment is:
- $ 2x + 2000 $.

The income from the first investment at 5% is:
- $ 0.05 \times x $.

The income from the second investment at 5% is:
- $ 0.05 \times (2x + 2000) $.

The total income from both investments is given as $2200, so the equation is:
\[
0.05 \times x + 0.05 \times (2x + 2000) = 2200.
\]

Now, I'll solve this equation.

### Step-by-Step Solution:

1. Distribute the 0.05 across the terms in the equation:
\[
0.05x + 0.05(2x + 2000) = 2200
\]
\[
0.05x + 0.1x + 100 = 2200
\]

2. Combine like terms:
\[
0.15x + 100 = 2200
\]

3. Subtract 100 from both sides:
\[
0.15x = 2100
\]

4. Divide both sides by 0.15 to find $ x $:
\[
x = \frac{2100}{0.15} = 14000
\]

So, Roberto invested **$14,000** at 5%.

Unfortunately, this value is not one of the options given in the image, suggesting there might be some issue with the problem setup. However, based on the problem statement and the calculations, $14,000 is the correct amount.

Would you like any further details on this? Here are some related questions for further practice:

1. If the interest rate had been 6%, how would the total income change?
2. What would happen if Roberto invested $3000 more instead of $2000 more?
3. How much would be invested if the total income was $2500 instead?
4. How does the final investment amount change if the interest rate changes to 4%?
5. What if Roberto only invested twice the initial amount without the additional $2000?

**Tip:** When working on investment problems, always clearly define variables and write out the total income formula. It helps avoid confusion when solving the equation.

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%?

Learn how to solve an investment problem involving Roberto, who invested at a 5% interest rate. This problem helps to understand linear equations, percentages, and simple interest calculations. The solution involves finding how much Roberto invested, given the total income from his investments.

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