Five years ago a man was seven times asold as his son. Five yeears hense, the father will be three time times as old as his son. Find their present ahes

Answer

To solve the problem, we will set up equations based on the information provided in the question. Let's break it down step by step.

### Step 1: Define Variables
Let the present age of the son be \( x \) years. Therefore, the present age of the father will be \( 7x \) years (since five years ago, the father was seven times as old as his son).

### Step 2: Set Up the First Equation
Five years ago, the son’s age was \( x - 5 \) and the father's age was \( 7x - 5 \). According to the problem, five years ago, the father was seven times as old as his son:
\[ 7x - 5 = 7(x - 5) \]

### Step 3: Simplify the First Equation
Expanding the right side:
\[ 7x - 5 = 7x - 35 \]
Now, we can simplify this equation by eliminating \( 7x \) from both sides:
\[ -5 = -35 \]
This equation does not provide any new information, so we will move on to the next condition.

### Step 4: Set Up the Second Equation
Now, consider the ages five years hence. The son's age will be \( x + 5 \) and the father's age will be \( 7x + 5 \). According to the problem, five years hence, the father will be three times as old as his son:
\[ 7x + 5 = 3(x + 5) \]

### Step 5: Simplify the Second Equation
Expanding the right side:
\[ 7x + 5 = 3x + 15 \]
Now, we can rearrange the equation to isolate \( x \):
\[ 7x - 3x = 15 - 5 \]
This simplifies to:
\[ 4x = 10 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 4:
\[ x = \frac{10}{4} = 2.5 \]

### Step 7: Calculate Present Ages
Now that we have \( x \), we can find the present ages:
- Present age of the son: \( x = 2.5 \) years
- Present age of the father: \( 7x = 7 \times 2.5 = 17.5 \) years

### Conclusion
Thus, the present age of the son is \( 2.5 \) years and the present age of the father is \( 17.5 \) years.