Four years ago a man was 6 times as old as his son. After 16 years he will be twice as old as his son. What is the present age of man and his son?

34, 9

33, 7

35, 5

36, 6

Let the present age of the man be \( M \) and the present age of his son be \( S \).

### Step 1: Setting up equations
We are given two conditions:

1. Four years ago, the man was 6 times as old as his son.
   - Four years ago, the man's age was \( M - 4 \) and the son's age was \( S - 4 \).
   - Therefore, \( M - 4 = 6(S - 4) \).

2. Sixteen years from now, the man will be twice as old as his son.
   - Sixteen years later, the man's age will be \( M + 16 \) and the son's age will be \( S + 16 \).
   - Therefore, \( M + 16 = 2(S + 16) \).

### Step 2: Solving the equations

#### Equation 1: \( M - 4 = 6(S - 4) \)
Expanding:
\[
M - 4 = 6S - 24
\]
\[
M = 6S - 20 \quad \text{(Equation 1)}
\]

#### Equation 2: \( M + 16 = 2(S + 16) \)
Expanding:
\[
M + 16 = 2S + 32
\]
\[
M = 2S + 16 \quad \text{(Equation 2)}
\]

### Step 3: Substituting Equation 2 into Equation 1
From Equation 2, \( M = 2S + 16 \). Substitute this into Equation 1:
\[
2S + 16 = 6S - 20
\]
Simplifying:
\[
16 + 20 = 6S - 2S
\]
\[
36 = 4S
\]
\[
S = 9
\]

### Step 4: Finding \( M \)
Substitute \( S = 9 \) into Equation 2:
\[
M = 2(9) + 16
\]
\[
M = 18 + 16 = 34
\]

### Step 5: Conclusion
The present age of the man is 34 and the present age of his son is 9. 

Thus, the correct answer is **34, 9**.

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Do you want more details or have any questions?

Here are 5 related questions you can try:

1. If a man is 5 times as old as his son today, how old was he when his son was born?
2. A man’s age is three times his son’s age. In how many years will the man be twice his son’s age?
3. A father’s age is 6 years more than twice his son’s age. If the son is 12, how old is the father?
4. The ratio of the ages of a father and his son is 5:2. If the father is 45, how old is the son?
5. A man is 4 years older than his son. In 10 years, their combined age will be 68. How old is each of them now?

**Tip:** When working with word problems involving ages, always create clear variables and set up equations based on the relationships provided.

Four years ago a man was 6 times as old as his son. After 16 years he will be twice as old as his son. What is the present age of the man and his son?

Learn how to solve an age problem where four years ago a man was 6 times as old as his son, and after 16 years he will be twice as old. Follow the step-by-step algebraic solution to find their current ages. Ideal for Grades 8-10.

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