Sal invested $17,000 in two accounts. If one account earned 4 percent interest and the other earned 6 percent interest and she had a total interest income of $770, how much did she invest in each account?

Let $ x $ be the amount Sal invested in the account with 4% interest. Then, the amount she invested in the account with 6% interest is $ 17000 - x $.

The interest earned from each account can be calculated as:

- For the account with 4% interest:  
  \[
  0.04x
  \]

- For the account with 6% interest:  
  \[
  0.06(17000 - x)
  \]

According to the problem, the total interest earned is $770. Therefore, we can set up the equation:

\[
0.04x + 0.06(17000 - x) = 770
\]

Let's solve this equation step-by-step:

1. Distribute the 0.06 in the second term:

\[
0.04x + 1020 - 0.06x = 770
\]

2. Combine like terms:

\[
-0.02x + 1020 = 770
\]

3. Subtract 1020 from both sides:

\[
-0.02x = 770 - 1020
\]

\[
-0.02x = -250
\]

4. Divide both sides by -0.02:

\[
x = \frac{-250}{-0.02} = 12500
\]

So, Sal invested $12,500 in the account with 4% interest.

Now, to find the amount invested in the account with 6% interest:

\[
17000 - 12500 = 4500
\]

Sal invested $4,500 in the account with 6% interest.

**Summary:**
- Amount invested in the account with 4% interest: **$12,500**
- Amount invested in the account with 6% interest: **$4,500**

Do you want more details or have any questions?

### Related Questions:
1. How do you verify the solution to investment problems involving multiple accounts?
2. What are some common methods to solve systems of linear equations in word problems?
3. How would the solution change if both accounts earned the same interest rate?
4. Can we use graphing methods to solve this problem?
5. What is the significance of understanding simple versus compound interest?

**Tip:** For investment problems, always double-check your final values by verifying that the sum of the individual interests matches the total given interest.

Discover how to solve an investment problem where $17,000 is split between two accounts earning 4% and 6% interest, with a total income of $770. This step-by-step solution covers the concepts of linear equations and simple interest calculations. Suitable for Grades 9-10.

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