A father distributed his total wealth to his two sons. The elder son recived 3/5 of the amount. The younger son received $30,000. How much wealth did the father have ?

Options

A. 15000
B. 45000
C. 60000
D. 75000

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Define the total wealth
Let the total wealth of the father be represented as \( x \) dollars.

### Step 2: Determine the amount received by the elder son
According to the problem, the elder son received \( \frac{3}{5} \) of the total wealth. Therefore, the amount received by the elder son can be expressed as:
\[ \text{Amount received by elder son} = \frac{3}{5}x \]

### Step 3: Determine the amount received by the younger son
The younger son received $30,000. Thus, we can write:
\[ \text{Amount received by younger son} = 30,000 \]

### Step 4: Set up the equation
Since the total wealth is distributed between the two sons, we can set up the equation:
\[ x = \frac{3}{5}x + 30,000 \]

### Step 5: Rearrange the equation
To isolate \( x \), we will move \( \frac{3}{5}x \) to the left side of the equation:
\[ x - \frac{3}{5}x = 30,000 \]

### Step 6: Simplify the left side
To simplify \( x - \frac{3}{5}x \), we need a common denominator:
\[ \frac{5x}{5} - \frac{3x}{5} = \frac{2x}{5} \]
Thus, the equation becomes:
\[ \frac{2x}{5} = 30,000 \]

### Step 7: Solve for \( x \)
To find \( x \), we will multiply both sides by 5:
\[ 2x = 30,000 \times 5 \]
Calculating the right side:
\[ 2x = 150,000 \]
Now, divide both sides by 2:
\[ x = \frac{150,000}{2} = 75,000 \]

### Conclusion
The total wealth of the father is \( x = 75,000 \) dollars.

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