Question 1184067: A state employees' pension fund invested a total of one million dollars in two accounts that earned 3.5% and 4.5% annual simple interest. At the end of the year, the total interest earned from the two investments was $43,000. How much was invested at each rate?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to solve this problem:
**Let:**
* 'x' be the amount invested at 3.5% interest.
* 'y' be the amount invested at 4.5% interest.
**Set up the equations:**
* **Equation 1 (Total investment):** x + y = 1,000,000
* **Equation 2 (Total interest):** 0.035x + 0.045y = 43,000
**Solve the equations:**
One way to solve this is using substitution:
1. **Solve Equation 1 for x:** x = 1,000,000 - y
2. **Substitute this value of x into Equation 2:**
0.035(1,000,000 - y) + 0.045y = 43,000
3. **Simplify and solve for y:**
35,000 - 0.035y + 0.045y = 43,000
0.01y = 8,000
y = 800,000
4. **Substitute the value of y back into Equation 1 to find x:**
x + 800,000 = 1,000,000
x = 200,000
**Answer:**
* $200,000 was invested at 3.5% interest.
* $800,000 was invested at 4.5% interest.
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