https://file.aiquickdraw.com/mathbot/file/1726973398285qc5n4531.jpg

This problem can be solved using a system of equations. Let's define the variables:

- Let $ x $ be the amount invested at 4%.
- Let $ 5000 - x $ be the amount invested at 11% (since the total investment is $5000).

The total interest earned from both accounts is $277.

The interest formula for simple interest is:
\[
I = P \cdot r \cdot t
\]
Where:
- $ I $ is the interest,
- $ P $ is the principal (amount invested),
- $ r $ is the rate (interest rate),
- $ t $ is the time in years (which is 1 year in this case).

For the account with 4% interest:
\[
\text{Interest from the 4% account} = x \cdot 0.04
\]

For the account with 11% interest:
\[
\text{Interest from the 11% account} = (5000 - x) \cdot 0.11
\]

The total interest is $277, so we can write the equation:
\[
x \cdot 0.04 + (5000 - x) \cdot 0.11 = 277
\]

Let's solve this equation.The amount invested in the account earning 4% interest is $3900.

Now, since Alma invested a total of $5000, the amount invested in the account earning 11% interest is:
\[
5000 - 3900 = 1100
\]

Thus:
- $3900 was invested at 4%.
- $1100 was invested at 11%.

Would you like further details or have any questions?

Here are 5 related questions:
1. How does simple interest differ from compound interest?
2. What would happen to the interest if the investment period was 2 years instead of 1?
3. Can we solve similar problems with more than two accounts?
4. What is the formula for calculating interest over multiple periods with different rates?
5. How would inflation impact the real value of interest earned?

**Tip:** To check your results, always substitute the values back into the original equation to confirm they satisfy all conditions.

Alma invests $5000 in two different accounts. The first account paid 4% simple interest, and the second account paid 11% simple interest. At the end of the year, she earned $277 in interest. How much was invested in each account?

Learn how to solve a simple interest investment problem where Alma invests $5000 in two accounts with different interest rates (4% and 11%) and earns $277 in interest at the end of the year. Step-by-step algebraic solution for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation