Five years ago I was 5 times older than my son.

In 8 years’ time I will be 3 times older than my son.

How old am I today?

Let's solve this step-by-step by setting up equations based on the information given.

### Step 1: Define Variables
Let:
- \( x \) be your current age.
- \( y \) be your son's current age.

### Step 2: Set Up Equations

1. **Five years ago**: You were \( x - 5 \) years old, and your son was \( y - 5 \) years old. According to the problem, five years ago you were 5 times older than your son:
   \[
   x - 5 = 5(y - 5)
   \]

2. **In eight years**: You will be \( x + 8 \) years old, and your son will be \( y + 8 \) years old. In eight years, you will be 3 times older than your son:
   \[
   x + 8 = 3(y + 8)
   \]

### Step 3: Solve the Equations

#### Expanding and simplifying Equation 1:
\[
x - 5 = 5y - 25
\]
Add 5 to both sides:
\[
x = 5y - 20 \quad \text{(Equation A)}
\]

#### Expanding and simplifying Equation 2:
\[
x + 8 = 3y + 24
\]
Subtract 8 from both sides:
\[
x = 3y + 16 \quad \text{(Equation B)}
\]

Now we have two equations:
1. \( x = 5y - 20 \)
2. \( x = 3y + 16 \)

#### Set Equations A and B equal to each other:
\[
5y - 20 = 3y + 16
\]
Subtract \( 3y \) from both sides:
\[
2y - 20 = 16
\]
Add 20 to both sides:
\[
2y = 36
\]
Divide by 2:
\[
y = 18
\]

#### Substitute \( y = 18 \) back into Equation A to find \( x \):
\[
x = 5(18) - 20
\]
\[
x = 90 - 20
\]
\[
x = 70
\]

### Answer
You are currently **70 years old**.

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Would you like further clarification on any of these steps?

---

1. How old will you and your son be in 10 years?
2. What if you were 6 times older than your son five years ago?
3. How would the answer change if you were twice your son's age in 8 years?
4. What if the problem involved 4 times the age five years ago?
5. Can we generalize this type of age problem for different multiples?

**Tip**: In age-related algebra problems, start by defining variables clearly and setting up equations based on the conditions given.

Five years ago I was 5 times older than my son. In 8 years’ time I will be 3 times older than my son. How old am I today?

Discover how to solve this age-related algebra problem: 'Five years ago I was 5 times older than my son. In 8 years, I will be 3 times older than him.' Includes step-by-step guidance on setting up and solving linear equations, ideal for students in Grades 8-10.

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