Problem 89 - Algebra A Combined Function

Question

Solve. See Example 22. The lowest elevation on Earth is -411 meters (that is, 411 meters below sea level) at the Dead Sea. If you are standing 316 meters above the Dead Sea, what is your elevation? (Source: National Geographic Society)

Step-by-Step Solution

Answer

Your elevation is -95 meters, or 95 meters below sea level.

Step 1: Understand the Problem

To solve the problem, we need to determine the elevation of a point that is 316 meters above the lowest elevation on Earth, which is -411 meters at the Dead Sea.

Step 2: Set Up the Equation

The elevation of the point where you are standing can be calculated by adding the distance you are above the Dead Sea to the Dead Sea's elevation. The equation to calculate this is given by: \[E = -411 + 316\]where \(E\) is the elevation of the point where you are standing.

Step 3: Perform the Calculation

Substitute the values into the equation and solve:\[E = -411 + 316 = -95\]

Step 4: Interpret the Result

The result of -95 meters indicates that you are 95 meters below sea level. This is your current elevation relative to sea level.

Key Concepts

Elevation Calculation

When we talk about elevation, we are referring to the height of a location relative to a baseline, commonly sea level. This allows us to understand how high or low something is compared to this universal reference point. In the given problem, the Dead Sea represents the lowest elevation at -411 meters, meaning it lies 411 meters below sea level.

To calculate elevation, you often need to add or subtract distances from a known reference point. If you're 316 meters above the Dead Sea, and the Dead Sea starts at -411 meters below sea level, you need to adjust for this height difference to find your exact elevation. The process of elevation calculation assists us in determining such differences in heights between two points.

Problem Solving Steps

Solving algebra word problems requires a structured approach. Here, we'll break it down into simple steps to follow.

• Understand the Problem: Identify what you know and what you need to find out. For the elevation problem, you know the Dead Sea's elevation and how much higher you are standing.
• Set Up the Equation: Convert the problem into an equation format using the known data points, which helps in finding the unknown.
• Perform the Calculation: Use mathematical operations to solve the equation. In our case, you add the height you're standing above the Dead Sea to its elevation.
• Interpret the Result: Understand what your solution represents and check if it makes sense. Here, a result of -95 meters means that despite being above the Dead Sea, you're still below sea level.

Following these steps systematically can simplify complex word problems.

Equation Setup

Setting up the correct equation is crucial in solving word problems. This involves translating the given information into a mathematical expression that can be solved to find the unknown.For our elevation problem, the equation needed is based on the relationship between your current position relative to the Dead Sea's known elevation. The formula is:\[ E = -411 + 316 \]Here, \(E\) represents your elevation. "-411" is used since the Dead Sea is 411 meters below sea level, and we "add" 316 meters because you are standing above it.

The equation setup forms the basis of your solution, guiding you through the steps necessary to find your answer. Properly setting up your equations can streamline the problem-solving process, making it much easier to find the right solution.