Susan placed $5,600 into three investments: Account A paid 10% simple interest, Account B paid 12% simple interest, and Account C paid 18% simple interest. The total interest earned after one year is $792. If the amount of money placed in Account C is $900 more than the amount placed in Account B, find the amount of each investment in dollars.


Let the amount of money placed in Account A, Account B, and Account C be denoted as $ A $, $ B $, and $ C $ respectively. Based on the problem, we can set up the following equations:

1. The total amount invested:
   \[
   A + B + C = 5600
   \]

2. The total interest earned from all three accounts:
   \[
   0.10A + 0.12B + 0.18C = 792
   \]

3. The amount placed in Account C is $900 more than the amount placed in Account B:
   \[
   C = B + 900
   \]

Now, we can solve this system of equations.

### Step 1: Substitute $ C = B + 900 $ into the first and second equations.

- From $ A + B + C = 5600 $, substitute $ C $:
  \[
  A + B + (B + 900) = 5600
  \]
  Simplifying:
  \[
  A + 2B + 900 = 5600
  \]
  \[
  A + 2B = 4700 \quad \text{(Equation 1)}
  \]

- From $ 0.10A + 0.12B + 0.18C = 792 $, substitute $ C $:
  \[
  0.10A + 0.12B + 0.18(B + 900) = 792
  \]
  Simplifying:
  \[
  0.10A + 0.12B + 0.18B + 0.18 \times 900 = 792
  \]
  \[
  0.10A + 0.30B + 162 = 792
  \]
  \[
  0.10A + 0.30B = 630 \quad \text{(Equation 2)}
  \]

### Step 2: Solve the system of two equations.

We now have the system of equations:
1. $ A + 2B = 4700 $
2. $ 0.10A + 0.30B = 630 $

#### Solve Equation 1 for $ A $:
\[
A = 4700 - 2B
\]

#### Substitute $ A = 4700 - 2B $ into Equation 2:
\[
0.10(4700 - 2B) + 0.30B = 630
\]
Simplifying:
\[
470 - 0.20B + 0.30B = 630
\]
\[
470 + 0.10B = 630
\]
\[
0.10B = 160
\]
\[
B = 1600
\]

#### Find $ A $ and $ C $:
- From $ A = 4700 - 2B $:
  \[
  A = 4700 - 2(1600) = 4700 - 3200 = 1500
  \]

- From $ C = B + 900 $:
  \[
  C = 1600 + 900 = 2500
  \]

### Final Answer:
- Amount in Account A: $1,500
- Amount in Account B: $1,600
- Amount in Account C: $2,500

Let me know if you need any more details or clarifications!

---

Here are 5 related questions to deepen your understanding:

1. What would happen to the total interest if the amount invested in Account C was increased by $500?
2. How would the solution change if the interest rate of Account B was reduced to 10%?
3. Can you express the total interest formula for $ n $ different accounts with various interest rates?
4. What is the total percentage return Susan earned on her total investment?
5. How would you solve this problem using matrices?

**Tip:** When dealing with multiple investments, always try to express relationships between accounts as equations to simplify solving.

Susan placed $5,600 into three investments: Account A paid 10% simple interest, Account B paid 12% simple interest, and Account C paid 18% simple interest. The total interest earned after one year is $792. If the amount of money placed in Account C is $900 more than the amount placed in Account B, find the amount of each investment in dollars.

Find out how to solve an investment allocation problem where $5,600 is distributed across three accounts earning different simple interest rates. Learn how to set up and solve a system of equations to calculate the amounts in each account, using interest formulas and algebraic techniques. This problem is ideal for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation