Solving a math word problem about ages using algebra.

Problem Statement:

Steve is 10 years older than Jamie, and one-half the age of Lynn. If their combined age is 46, how old is each person?

Solution:

#### Step 1: Define Variables
Let:
- \( x \) = Steve's age.
- \( x - 10 \) = Jamie's age (since Steve is 10 years older than Jamie).
- \( 2x \) = Lynn's age (since Steve is one-half the age of Lynn).

#### Step 2: Write the Equation for Combined Age
The problem states that the combined age of Steve, Jamie, and Lynn is 46. Therefore, we can write the equation:
\[
x + (x - 10) + 2x = 46
\]

#### Step 3: Simplify the Equation
Combine like terms:
\[
x + x - 10 + 2x = 46
\]
\[
4x - 10 = 46
\]

#### Step 4: Solve for \( x \)
Add 10 to both sides of the equation:
\[
4x = 56
\]

Divide both sides by 4:
\[
x = 14
\]

#### Step 5: Determine the Ages of Each Person
- Steve's age (\( x \)) = 14.
- Jamie's age (\( x - 10 \)) = \( 14 - 10 = 4 \).
- Lynn's age (\( 2x \)) = \( 2 \times 14 = 28 \).

#### Step 6: Verify the Solution
Check the combined age:
\[
\text{Steve's age} + \text{Jamie's age} + \text{Lynn's age} = 14 + 4 + 28 = 46
\]
The combined age is indeed 46, so the solution is correct.

Final Answer:

\[
\boxed{14, 4, 28}
\]

Steve is 14 years old, Jamie is 4 years old, and Lynn is 28 years old.