The present age of a father is equal to the sum of the ages of his 5 children. 12 years hence, the sum of the ages of his children will be twice the ages of their father. Find the present age of the father.

Answer

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

### Step 1: Define Variables
Let the present age of the father be \( F \) and the present age of one child be \( C \). Since there are 5 children, the total present age of the children will be \( 5C \).

### Step 2: Set Up the First Equation
According to the problem, the present age of the father is equal to the sum of the ages of his 5 children:
\[ F = 5C \quad \text{(1)} \]

### Step 3: Set Up the Second Equation
The problem states that 12 years from now, the sum of the ages of the children will be twice the age of the father. In 12 years, the age of the father will be \( F + 12 \) and the age of each child will be \( C + 12 \). Therefore, the total age of the children in 12 years will be:
\[ 5(C + 12) = 5C + 60 \]
According to the problem, this total will be twice the father's age at that time:
\[ 5C + 60 = 2(F + 12) \quad \text{(2)} \]

### Step 4: Substitute Equation (1) into Equation (2)
From equation (1), we know \( F = 5C \). Substitute this into equation (2):
\[ 5C + 60 = 2(5C + 12) \]

### Step 5: Simplify the Equation
Now simplify the equation:
\[ 5C + 60 = 10C + 24 \]

### Step 6: Rearrange the Equation
Rearranging gives:
\[ 60 - 24 = 10C - 5C \]
\[ 36 = 5C \]

### Step 7: Solve for \( C \)
Now, divide both sides by 5:
\[ C = \frac{36}{5} = 7.2 \]

### Step 8: Find the Present Age of the Father
Now substitute \( C \) back into equation (1) to find \( F \):
\[ F = 5C = 5 \times 7.2 = 36 \]

Thus, the present age of the father is \( 36 \) years.

### Final Answer
The present age of the father is **36 years**.

---