To solve this problem, we set up a system of equations based on the information provided:

Let:

• $x$ = amount invested at 5%
• $y$ = amount invested at 8%

We know:

1. The total investment is $5,000: $x + y = 5000$
2. The total interest earned from both accounts is $340: $0.05x + 0.08y = 340$

Solving the System of Equations

Step 1: Solve for $y$ in terms of $x$ using the first equation

From $x + y = 5000$: $y = 5000 - x$

Step 2: Substitute $y = 5000 - x$ into the second equation

Substitute into $0.05x + 0.08y = 340$: $0.05x + 0.08(5000 - x) = 340$

Expanding and simplifying: $0.05x + 400 - 0.08x = 340$ $-0.03x = -60$ $x = \frac{-60}{-0.03} = 2000$

Step 3: Substitute $x = 2000$ back into $y = 5000 - x$

$y = 5000 - 2000 = 3000$

Solution

• $x = 2000$: $2,000 was invested at 5%
• $y = 3000$: $3,000 was invested at 8%

This matches the solution you provided.

Would you like a detailed breakdown of the steps?

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Related questions:

1. What would the investments be if the total interest was different?
2. How does changing the interest rates affect the amounts invested?
3. What happens if the total investment is altered but interest rates remain the same?
4. Can we solve similar problems with different percentages?
5. How would the approach change if one interest rate was compounded?

Tip: Setting up equations based on given information is essential for solving investment problems effectively.