A part of P70,000 is invested in 7% and the rest of 8% preferred stocks, Find how much is invested at each rate if the income from the 8% shares of stock exceeds the income from the 7% stock by 1,100.

Let's denote the amount invested at 7% as \( x \) and the amount invested at 8% as \( 70,000 - x \) (since the total investment is \( 70,000 \)).

The income from the 7% investment is:
\[
0.07x
\]

The income from the 8% investment is:
\[
0.08(70,000 - x)
\]

According to the problem, the income from the 8% shares exceeds the income from the 7% shares by 1,100. This gives us the equation:
\[
0.08(70,000 - x) = 0.07x + 1,100
\]

Now, let's solve this equation step by step:

1. Expand the left side:
   \[
   0.08 \times 70,000 - 0.08x = 0.07x + 1,100
   \]
   \[
   5,600 - 0.08x = 0.07x + 1,100
   \]

2. Combine like terms by adding \( 0.08x \) to both sides:
   \[
   5,600 = 0.15x + 1,100
   \]

3. Subtract \( 1,100 \) from both sides:
   \[
   4,500 = 0.15x
   \]

4. Solve for \( x \) by dividing both sides by 0.15:
   \[
   x = \frac{4,500}{0.15} = 30,000
   \]

Thus, \( 30,000 \) pesos is invested at 7%.

The amount invested at 8% is:
\[
70,000 - 30,000 = 40,000
\]

**Summary:**
- **Amount invested at 7%:** 30,000 pesos
- **Amount invested at 8%:** 40,000 pesos

Would you like more details, or do you have any questions? 

Here are 5 related questions:
1. How would the solution change if the total investment was \( 80,000 \) pesos?
2. What if the income difference was \( 1,500 \) pesos instead of \( 1,100 \) pesos?
3. How much total income is generated from both investments combined?
4. How can you express the income difference as a percentage of the total income?
5. What would be the result if the interest rates were swapped?

**Tip:** Always double-check the terms of the problem to ensure the correct setup of equations.

Learn how to solve an investment problem involving 7% and 8% preferred stocks. Calculate the amounts invested at each rate given specific income conditions. Suitable for Grades 9-12.

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