Sam is twenty-six years older than Brian. Eight years from now, Sam will be three times as old as Brian. Find their present age

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

### Step 1: Define Variables
- Let \( S \) represent Sam's current age.
- Let \( B \) represent Brian's current age.

### Step 2: Translate the Problem into Equations

1. **Sam is twenty-six years older than Brian**:
   \[
   S = B + 26
   \]

2. **Eight years from now, Sam will be three times as old as Brian**:
   - Eight years from now, Sam's age will be \( S + 8 \).
   - Eight years from now, Brian's age will be \( B + 8 \).
   - The equation based on the second condition is:
   \[
   S + 8 = 3(B + 8)
   \]

### Step 3: Solve the Equations

First, substitute the expression for \( S \) from the first equation into the second equation:

\[
(B + 26) + 8 = 3(B + 8)
\]

Simplify the equation:

\[
B + 34 = 3B + 24
\]

Rearrange the equation to group the \( B \) terms on one side:

\[
34 - 24 = 3B - B
\]

\[
10 = 2B
\]

Divide by 2 to find \( B \):

\[
B = 5
\]

Now, find \( S \) using the first equation:

\[
S = B + 26 = 5 + 26 = 31
\]

### Step 4: Conclusion

- **Brian's current age**: \( B = 5 \) years
- **Sam's current age**: \( S = 31 \) years

So, Brian is **5 years old** and Sam is **31 years old**.

Would you like further details or have any questions about this solution?

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Here are some related questions that expand on this topic:

1. What will be the ages of Sam and Brian 15 years from now?
2. If Sam was 10 years younger, how would that affect the future age ratio given?
3. How do you solve simultaneous equations involving word problems?
4. What strategies can help solve more complex age-related algebra problems?
5. If Sam's age is reduced by half, how does this affect the relationship described?

**Tip:** When solving age-related problems, always double-check the conditions given for "years from now" or "years ago" to ensure accuracy in setting up equations.

Learn how to solve the problem involving Sam and Brian's ages with a step-by-step solution. This problem covers algebraic concepts such as linear equations and is suitable for students in Grades 7-9.

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