5 years later, Sam's age is equal to 2 times Samantha's age. 5 years ago, Sam's age is equal to 3 times Samantha's age. If you remove 10 years from Sam's age, and add 10 years to Samantha's age, they will both be equal. What is Samantha's age?

Let's denote Sam's current age by \( S \) and Samantha's current age by \( T \).

The problem gives us three conditions:

1. In 5 years, Sam's age will be twice Samantha's age.
2. 5 years ago, Sam's age was three times Samantha's age.
3. If you remove 10 years from Sam's age and add 10 years to Samantha's age, they will both be equal.

Let's translate these conditions into equations.

### Step-by-Step Solution:

1. **In 5 years:**
   \[
   S + 5 = 2(T + 5)
   \]
   Simplifying this equation:
   \[
   S + 5 = 2T + 10
   \]
   \[
   S - 2T = 5 \quad \text{(Equation 1)}
   \]

2. **5 years ago:**
   \[
   S - 5 = 3(T - 5)
   \]
   Simplifying this equation:
   \[
   S - 5 = 3T - 15
   \]
   \[
   S - 3T = -10 \quad \text{(Equation 2)}
   \]

3. **Removing 10 years from Sam's age and adding 10 years to Samantha's age:**
   \[
   S - 10 = T + 10
   \]
   Simplifying this equation:
   \[
   S - T = 20 \quad \text{(Equation 3)}
   \]

We now have a system of three equations:

\[
\begin{cases}
S - 2T = 5 \quad \text{(Equation 1)} \\
S - 3T = -10 \quad \text{(Equation 2)} \\
S - T = 20 \quad \text{(Equation 3)}
\end{cases}
\]

To solve this system, we can start by subtracting Equation 2 from Equation 1 to eliminate \( S \):

\[
(S - 2T) - (S - 3T) = 5 - (-10)
\]
\[
S - 2T - S + 3T = 15
\]
\[
T = 15
\]

Now that we have \( T = 15 \), we can substitute this value back into Equation 3 to find \( S \):

\[
S - 15 = 20
\]
\[
S = 35
\]

### Solution:

Samantha's age (\( T \)) is \( 15 \) years.

Would you like further details or have any questions?

### Related Questions:

1. If 3 years from now, John’s age will be 4 times Mary’s age, how old is Mary now if John is currently 6 years older than Mary?
2. Solve for current ages if 4 years from now, A’s age will be 3 times B’s age, and A is currently 2 years younger than B.
3. If the sum of the ages of Anne and Bob is 50 years, and Anne is 10 years older than Bob, how old is Bob?
4. If in 7 years, Carla will be twice as old as she was 3 years ago, how old is Carla now?
5. Given that the current age of David is 4 times the age of Emma, and in 6 years, David’s age will be twice the age of Emma, what are their current ages?
6. If the difference between Alan and Brian’s ages is 12 years, and 10 years ago Alan was twice as old as Brian, what are their current ages?
7. If Emily is currently 10 years older than Jake, and in 8 years Emily will be twice as old as Jake, how old are they now?
8. Solve for current ages if Mark is 5 years older than Nick, and in 3 years Mark will be twice as old as Nick was 5 years ago.

### Tip:

When solving age-related word problems, clearly define your variables and translate the problem into equations step-by-step.

Learn how to solve the age problem involving Sam and Samantha's ages using linear equations and age-related conditions. This problem requires understanding relationships between ages and solving simultaneous equations. Suitable for Grades 7-9 students.

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