A businessman earned 69,000 from two kinds of bonds, one of which yielded 3% a year and the other yielded 5%. How much did he earns from each kind of bond, if his 3% bond earned P7,000 more than the other?

Let's denote:

- The amount invested in the bond yielding 3% as \( x \) pesos.
- The amount invested in the bond yielding 5% as \( y \) pesos.

According to the problem, the businessman earned a total of 69,000 pesos from both bonds, and the earnings from the 3% bond were 7,000 pesos more than the earnings from the 5% bond.

### Step 1: Write the equations
1. The earnings from the 3% bond:
   \[
   0.03x
   \]

2. The earnings from the 5% bond:
   \[
   0.05y
   \]

Given that the earnings from the 3% bond are 7,000 pesos more than the 5% bond, we can write:
\[
0.03x = 0.05y + 7,000
\]

The total earnings from both bonds is 69,000 pesos:
\[
0.03x + 0.05y = 69,000
\]

### Step 2: Solve the system of equations
We have two equations:
\[
0.03x = 0.05y + 7,000
\]
\[
0.03x + 0.05y = 69,000
\]

#### Substituting the first equation into the second equation:
From the first equation:
\[
0.03x - 0.05y = 7,000 \quad \text{(Equation 1)}
\]

Now substitute \( 0.03x = 0.05y + 7,000 \) into the second equation:
\[
(0.05y + 7,000) + 0.05y = 69,000
\]



Explore how to solve a linear equations problem involving a businessman's earnings from two types of bonds yielding 3% and 5%. Understand the mathematical concepts of linear equations and how to apply them to financial scenarios. Suitable for students in Grades 9-12.

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