A man invested Php100, 000. He put part of it in the bank at 5% interest. On the other hand, he invested the remainder in bonds with a 9% yearly return. How much did he put in the bank if his yearly income from the two investments was Php7, 400

Let's solve this problem step-by-step by setting up an equation based on the information given:

### Variables:
Let:
- \( x \) = the amount of money invested in the bank (at 5% interest).
- \( 100,000 - x \) = the amount of money invested in bonds (at 9% yearly return).

### Interest Earned:
- The interest from the bank investment at 5% = \( 0.05 \times x \).
- The interest from the bond investment at 9% = \( 0.09 \times (100,000 - x) \).

The total yearly income from both investments is Php 7,400. So, the equation is:

\[
0.05x + 0.09(100,000 - x) = 7,400
\]

### Solving the Equation:
Now let's solve for \( x \).

1. Distribute the 0.09 on the second term:
   \[
   0.05x + 0.09(100,000) - 0.09x = 7,400
   \]
   \[
   0.05x + 9,000 - 0.09x = 7,400
   \]

2. Combine like terms:
   \[
   (0.05x - 0.09x) + 9,000 = 7,400
   \]
   \[
   -0.04x + 9,000 = 7,400
   \]

3. Subtract 9,000 from both sides:
   \[
   -0.04x = 7,400 - 9,000
   \]
   \[
   -0.04x = -1,600
   \]

4. Divide both sides by -0.04:
   \[
   x = \frac{-1,600}{-0.04}
   \]
   \[
   x = 40,000
   \]

### Conclusion:
The man invested **Php 40,000** in the bank at 5% interest.

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

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Here are 5 related questions to expand this topic:
1. How much did the man invest in bonds?
2. What would the income be if he invested Php 50,000 in the bank and Php 50,000 in bonds?
3. How would the total yearly income change if the bank interest rate was increased to 6%?
4. What is the total return percentage on his investment based on the Php 7,400 return?
5. What if the man invested all Php 100,000 in the bank at 5%, how much income would he earn?

**Tip:** Always check if your equation accurately reflects all the conditions of the problem before solving it.

A man invested Php100,000. He put part of it in the bank at 5% interest. On the other hand, he invested the remainder in bonds with a 9% yearly return. How much did he put in the bank if his yearly income from the two investments was Php7,400?

Learn how to calculate how much a man invested in the bank at 5% interest and in bonds at 9% yearly return. This problem involves solving linear equations based on total interest income of Php7,400. Suitable for students in Grades 8-10.

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