Tom invests part of Php.12,000 in a stock that pays 5% annually and the rest in a 
mutual fund that pays 8% annually. If Tom earns Php.720 in interest after one year, 
how much did he invest in each?

Let's denote:
- \( x \) as the amount Tom invested in the stock that pays 5% annually.
- \( 12,000 - x \) as the amount he invested in the mutual fund that pays 8% annually.

### Step 1: Set up the equation
Tom earns Php 720 in total interest after one year. The total interest from both investments can be written as:

\[
0.05x + 0.08(12,000 - x) = 720
\]

### Step 2: Simplify the equation
Distribute the 0.08 on the second term:

\[
0.05x + 0.08(12,000) - 0.08x = 720
\]

\[
0.05x + 960 - 0.08x = 720
\]

### Step 3: Combine like terms
Combine the terms involving \( x \):

\[
-0.03x + 960 = 720
\]

### Step 4: Solve for \( x \)
Subtract 960 from both sides:

\[
-0.03x = 720 - 960
\]

\[
-0.03x = -240
\]

Now, divide by -0.03:

\[
x = \frac{-240}{-0.03} = 8,000
\]

### Step 5: Find the amount invested in the mutual fund
Since Tom invested Php 8,000 in the stock, the amount he invested in the mutual fund is:

\[
12,000 - 8,000 = 4,000
\]

### Final Answer:
- Tom invested Php 8,000 in the stock that pays 5%.
- He invested Php 4,000 in the mutual fund that pays 8%.

Would you like a deeper explanation on any step or have other questions?

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Here are 5 questions that might interest you:
1. How would the calculation change if the interest rates were different?
2. What if Tom wanted to earn Php 1,000 in interest? How much should he invest in each?
3. How does the overall interest rate affect the total interest earned?
4. What is the difference between simple and compound interest in such investments?
5. How can Tom optimize his investment strategy to earn more interest over time?

**Tip:** When solving problems involving investments, always double-check the interest rates and terms to avoid confusion!

Tom invests part of Php.12,000 in a stock that pays 5% annually and the rest in a mutual fund that pays 8% annually. If Tom earns Php.720 in interest after one year, how much did he invest in each?

Learn how to calculate the amounts Tom invested in a stock and mutual fund based on an interest problem. This problem uses algebraic concepts like linear equations and simple interest to determine the investment distribution. Suitable for Grades 8-10 students.

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