If twice the sons age in years is added to the fathers age, the sum is 70. But if twice the others age is added to the sons age, the sum is 95. Find the ages of father and son.

Answer

To solve the problem, we will define the variables and set up the equations based on the information provided in the question.

### Step 1: Define the Variables
Let:
- \( x \) = age of the son (in years)
- \( y \) = age of the father (in years)

### Step 2: Set Up the Equations
According to the problem:
1. Twice the son's age added to the father's age equals 70:
\[ 2x + y = 70 \quad \text{(Equation 1)} \]

2. The son's age added to twice the father's age equals 95:
\[ x + 2y = 95 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
We will solve these two equations simultaneously.

**From Equation 1:**
\[ y = 70 - 2x \quad \text{(Substituting for } y\text{)} \]

**Substituting \( y \) in Equation 2:**
\[ x + 2(70 - 2x) = 95 \]
\[ x + 140 - 4x = 95 \]
\[ 140 - 3x = 95 \]
\[ -3x = 95 - 140 \]
\[ -3x = -45 \]
\[ x = 15 \]

### Step 4: Find the Father's Age
Now that we have the son's age \( x \):
\[ y = 70 - 2(15) \]
\[ y = 70 - 30 \]
\[ y = 40 \]

### Conclusion
The ages are:
- Son's age = 15 years
- Father's age = 40 years