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The problem involves students hiking 38 km over three days. Here's the breakdown:

Let:
- \( x \) represent the distance hiked on the second day.
- The first day, they hiked \( 3x - 1 \) km (3 times the second day minus 1 km).
- The third day, they hiked \( (3x - 1) - 2 = 3x - 3 \) km (2 km less than the first day).

The total distance over the three days is 38 km, so we can write the equation:

\[
(3x - 1) + x + (3x - 3) = 38
\]

Simplifying:

\[
7x - 4 = 38
\]

Adding 4 to both sides:

\[
7x = 42
\]

Dividing by 7:

\[
x = 6
\]

So the second day they hiked 6 km. The distance on the first day is:

\[
3x - 1 = 3(6) - 1 = 18 - 1 = 17 \text{ km}
\]

Thus, the students hiked **17 km on the first day**.

Answer: \( \boxed{C} \).

Would you like further details or have any questions?

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Here are 5 related questions to deepen your understanding:
1. How would the answer change if they hiked 4 km less than 3 times the second day’s distance on the first day?
2. If the total distance hiked was 45 km instead of 38 km, how would the calculations change?
3. What if the second day's hike was 5 km instead of the variable \( x \)?
4. Can you rewrite the problem as a system of equations for each day's hike?
5. How would the problem change if the second day’s hike was half the first day’s hike?

**Tip**: Setting up equations based on word problems simplifies solving them efficiently!

A group of students hiked 38 km over three days. The first day, the students hiked 1 km less than 3 times as far as they hiked the second day. The third day, they hiked 2 km less than the first day. How far did the students hike the first day?

Learn how to solve a 3-day hiking word problem using algebra, covering the concept of setting up linear equations to find distances. The problem involves students hiking 38 km over three days with varied distances each day.

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