Henry's father is now twice as old as Henry is. He was four times as old 16 years ago. How old are they now?

Let's define the variables:

- Let \( h \) be Henry's current age.
- Let \( f \) be Henry's father's current age.

### Step 1: Set up the equations
According to the problem, we have two conditions:

1. **Henry's father is now twice as old as Henry**:
   \[
   f = 2h
   \]

2. **Henry's father was four times as old as Henry 16 years ago**:
   \[
   f - 16 = 4(h - 16)
   \]

### Step 2: Solve the system of equations
We can substitute the first equation \( f = 2h \) into the second equation.

Substitute \( f = 2h \) into \( f - 16 = 4(h - 16) \):

\[
2h - 16 = 4(h - 16)
\]

Now, expand and simplify:

\[
2h - 16 = 4h - 64
\]

Subtract \( 2h \) from both sides:

\[
-16 = 2h - 64
\]

Add 64 to both sides:

\[
48 = 2h
\]

Divide both sides by 2:

\[
h = 24
\]

Now that we have Henry's age, we can find his father's age using \( f = 2h \):

\[
f = 2(24) = 48
\]

### Conclusion
- Henry is **24 years old**.
- Henry's father is **48 years old**.

Would you like any further explanation or details on this solution?

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Here are 5 related questions:

1. How would the problem change if Henry's father was 3 times as old as Henry 16 years ago?
2. What if Henry was twice as old as he is now? How old would his father be?
3. Can you find a general solution if Henry's father was \( n \) times Henry's age 16 years ago?
4. How does the solution change if instead of 16 years ago, it was 20 years ago?
5. What if the problem stated that Henry’s father is now three times as old as Henry?

**Tip:** Always check your solutions by substituting them back into the original problem conditions.

Explore how to solve age-related problems involving ratios and equations. Learn step-by-step how to determine Henry and his father's current ages based on given conditions. Suitable for students in Grades 6-8.

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