Peter ate 4n apples.Mary ate 2 fewer apples than Peter.James only ate half as many as Mary.Find the number of apples that James ate in terms of n.

1. Break Down the Problem

1. Identify how many apples Peter ate: $4n$.
2. Determine how many apples Mary ate, given she ate 2 fewer than Peter.
3. Calculate how many apples James ate, given he ate half as many as Mary.

2. Relevant Concepts

• For Mary: $\text{Mary's apples} = \text{Peter's apples} - 2$
• For James: $\text{James' apples} = \frac{1}{2} \times \text{Mary's apples}$

3. Analysis and Detail

1. Calculate the number of apples Mary ate: $\text{Mary's apples} = 4n - 2$

2. Calculate the number of apples James ate: $\text{James' apples} = \frac{1}{2} \times (4n - 2)$ $= \frac{4n - 2}{2} = 2n - 1$

4. Verify and Summarize

1. Verify the formula step for Mary:
   • If Peter ate $4n$, then Mary ate $4n - 2$ which checks out.
2. Verify the formula step for James:
   • If Mary ate $4n - 2$, then James eating half means $2n - 1$.

Final Answer

James ate $2n - 1$ apples.