Name Trip to the Mountains The Hiking club is on a trip to hike up a mountain. Problem 1 The members increased their elevation 290 feet during their hike this morning. Now they are at an elevation of 450 feet. a. Explain how to find their elevation before the hike. b. Han says the equation \( e +290=450 \) describes the situation. What does the variable \( e \) represent? c. Han says that he can rewrite his equation as \( e=450+(-290) \) to solve for \( e \). Compare Han's strategy to your strategy for finding the beginning elevation.

Let's break down the problem step by step. ### Part a: Finding the Elevation Before the Hike To find the elevation before the hike, we need to consider the total elevation gained during the hike and the current elevation. The current elevation after the hike is 450 feet, and the members increased their elevation by 290 feet. To find the elevation before the hike, we can use the following formula: \[ \text{Elevation before hike} = \text{Current elevation} - \text{Elevation gained} \] Substituting the known values: \[ \text{Elevation before hike} = 450 - 290 \] Now, we can calculate this value. ### Part b: Understanding the Equation In Han's equation \( e + 290 = 450 \): - The variable \( e \) represents the elevation before the hike. This is because the equation states that if you add the elevation gained (290 feet) to the elevation before the hike (\( e \)), you will arrive at the current elevation (450 feet). ### Part c: Comparing Strategies Han's strategy involves rewriting the equation to isolate \( e \): \[ e = 450 + (-290) \] This is equivalent to subtracting 290 from 450, which is the same as our initial approach. Both strategies ultimately lead to the same result, but they are expressed differently: 1. **My strategy** directly uses subtraction to find the elevation before the hike. 2. **Han's strategy** uses the concept of adding a negative number, which is mathematically valid but may be less intuitive for some. Now, let's calculate the elevation before the hike using my strategy: \[ \text{Elevation before hike} = 450 - 290 \] Calculating this gives: \[ \text{Elevation before hike} = 160 \] Thus, the elevation before the hike was 160 feet. In summary: - The elevation before the hike is 160 feet. - \( e \) represents the elevation before the hike. - Both strategies are valid and lead to the same conclusion, though they approach the problem differently.