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!

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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.