Maricopa success scholarship fund receives a gift of $75,000. The money is invested in stocks bonds and CDs stocks pay 6.6% interest bonds pay 4.2 interest in CD pay 3% interest Maricopa success invest $20,000 more in bond then CD the annual income from the investments is $3450. How much was invested in each account

To determine how much was invested in each account (stocks, bonds, and CDs), we need to set up a system of equations based on the given information.

Let's define:
- $ S $ as the amount invested in stocks.
- $ B $ as the amount invested in bonds.
- $ C $ as the amount invested in CDs.

From the problem, we know the following:

1. The total investment is $75,000:
\[ S + B + C = 75,000 \]

2. The annual income from the investments is $3450:
\[ 0.066S + 0.042B + 0.03C = 3450 \]

3. Maricopa Success invested $20,000 more in bonds than in CDs:
\[ B = C + 20,000 \]

Now, we have a system of three equations:

1. $ S + B + C = 75,000 $
2. $ 0.066S + 0.042B + 0.03C = 3450 $
3. $ B = C + 20,000 $

We will solve this system step by step.

### Step 1: Substitute $ B $ in terms of $ C $

From equation (3), we have:
\[ B = C + 20,000 \]

### Step 2: Substitute $ B $ into equations (1) and (2)

Substitute $ B $ in equation (1):
\[ S + (C + 20,000) + C = 75,000 \]
\[ S + 2C + 20,000 = 75,000 \]
\[ S + 2C = 55,000 \]
\[ S = 55,000 - 2C \]

Substitute $ B $ in equation (2):
\[ 0.066S + 0.042(C + 20,000) + 0.03C = 3450 \]
\[ 0.066S + 0.042C + 840 + 0.03C = 3450 \]
\[ 0.066S + 0.072C + 840 = 3450 \]
\[ 0.066S + 0.072C = 2610 \]
\[ S = \frac{2610 - 0.072C}{0.066} \]

### Step 3: Solve for $ C $

Set the expressions for $ S $ equal to each other:
\[ 55,000 - 2C = \frac{2610 - 0.072C}{0.066} \]

Multiply both sides by 0.066 to clear the fraction:
\[ 0.066(55,000 - 2C) = 2610 - 0.072C \]
\[ 3630 - 0.132C = 2610 - 0.072C \]
\[ 3630 - 2610 = 0.132C - 0.072C \]
\[ 1020 = 0.06C \]
\[ C = \frac{1020}{0.06} \]
\[ C = 17,000 \]

### Step 4: Solve for $ B $

Using $ C = 17,000 $ in equation (3):
\[ B = C + 20,000 \]
\[ B = 17,000 + 20,000 \]
\[ B = 37,000 \]

### Step 5: Solve for $ S $

Using $ C = 17,000 $ in equation (1):
\[ S + B + C = 75,000 \]
\[ S + 37,000 + 17,000 = 75,000 \]
\[ S + 54,000 = 75,000 \]
\[ S = 21,000 \]

### Conclusion

The amounts invested in each account are:
- Stocks: $21,000
- Bonds: $37,000
- CDs: $17,000

Would you like further details on this solution, or do you have any questions?

Here are some related questions:

1. How would the solution change if the total investment was different?
2. What if the interest rates for stocks, bonds, or CDs were different?
3. How would the solution change if Maricopa Success invested a different amount more in bonds than in CDs?
4. What is the impact of changing the annual income requirement?
5. How can we use a different method (e.g., matrices) to solve the same problem?
6. What are the potential risks and benefits of investing in stocks, bonds, and CDs?
7. How can diversification in investments impact overall returns and risk?
8. What are some other investment options Maricopa Success could consider for their funds?

**Tip:** When solving systems of equations, it helps to isolate one variable and substitute it back into the other equations to simplify the process.

Learn how to allocate investments in stocks, bonds, and CDs with a detailed solution. This problem involves solving a system of equations to determine how much was invested in each account. Suitable for Grades 9-12.

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