Question 1170948
Let's solve this problem step-by-step.

**1. Define Variables:**

* Let 'x' be the number of units of government bonds.
* Let 'y' be the number of units of stocks.

**2. Set Up Equations:**

* **Total Investment:** The total investment is P 50,000, and each unit is P 100.00.
    * 100x + 100y = 50,000
    * Divide by 100: x + y = 500  (Equation 1)

* **Annual Return:** The desired overall return is 5% of P 50,000, which is P 2,500.
    * 4.5% of (100x) + 6% of (100y) = 2,500
    * 4.5x + 6y = 2,500  (Equation 2)

**3. Solve the System of Equations:**

We can solve this system using substitution or elimination. Let's use substitution:

* From Equation 1: y = 500 - x

* Substitute this into Equation 2:
    * 4.5x + 6(500 - x) = 2,500
    * 4.5x + 3,000 - 6x = 2,500
    * -1.5x = -500
    * x = 500 / 1.5 = 1000 / 3 ≈ 333.33

Since the investments are in whole units, we need to round to the nearest whole number. We'll round down to minimize stock investment, so x = 333.

* Substitute x = 333 back into Equation 1:
    * 333 + y = 500
    * y = 500 - 333 = 167

**4. Check the Solution:**

* Total Investment: 333(100) + 167(100) = 33,300 + 16,700 = 50,000 (Correct)

* Annual Return:
    * (0.045 * 33,300) + (0.06 * 16,700) = 1,498.50 + 1,002 = 2,500.50

The return is slightly over P 2,500, which is acceptable.

**5. Conclusion:**

The man should purchase:

* **333 units of government bonds (P 33,300)**
* **167 units of stocks (P 16,700)**