Problem 101 - Elementary and Intermediate Algebra

Question

Geography. The elevation of Death Valley, California, is 282 feet below sea level. The elevation of the Dead Sea in Israel is \(1,312\) feet below sea level. Find the difference in their elevations.

Step-by-Step Solution

Answer

The difference in elevation is 1,030 feet.

Step 1: Identify the Elevations

The elevation of Death Valley is 282 feet below sea level, and the elevation of the Dead Sea is 1,312 feet below sea level.

Step 2: Set Up the Subtraction

To find the difference, subtract the elevation of Death Valley from the elevation of the Dead Sea: \[ 1312 - 282 \]

Step 3: Perform the Subtraction

Subtract the two elevations to find the difference:\[ 1312 - 282 = 1030 \]

Step 4: Interpret the Result

The difference in elevation between the Dead Sea and Death Valley is 1,030 feet.

Key Concepts

Elevation Calculation

To understand elevation calculation, especially when dealing with negative elevation, it's crucial to grasp how elevations are noted in terms of how far above or below sea level they are. Elevation is the height of a point on the Earth's surface relative to sea level. Typically, when we say something is below sea level, it means it has a negative elevation.
For example, in our exercise, Death Valley and the Dead Sea both have negative elevations because they are located below sea level. Death Valley is at -282 feet and the Dead Sea is at -1312 feet. Calculating the difference in elevation involves finding out how much more below sea level one point is compared to another.
When performing calculations, it's essential to pay attention to the positive and negative signs. This ensures accuracy, as a mixed understanding of these values could lead to the wrong answers. Remember, negative elevation means below sea level, and when comparing two negatives, the larger absolute value indicates a lower position.

Step by Step Solution

Providing a step by step solution for mathematical problems like these makes the process more manageable and easier to understand.
The solution to the elevation difference problem involved several clear steps:

• Identify the Elevations: Begin by clearly noting the elevation values for both locations. For Death Valley, it is -282 ft, and for the Dead Sea, it is -1312 ft.
• Setup the Subtraction: Arrange the subtraction problem by setting the two elevations up as: \[1312 - 282\]
• Perform the Calculation: Simply subtract the elevation of Death Valley from the elevation of the Dead Sea. Using a calculator or mental arithmetic can help you solve:\[1312 - 282 = 1030\]
• Interpret the Result: Understand that the difference means the Dead Sea is 1030 feet more below sea level than Death Valley.

Keeping solutions step-by-step not only aids in solving specific problems but also helps in building a structured way of approaching mathematical tasks.

Mathematical Problem Solving

Mathematical problem solving is a critical skill that helps in not just academic success but also in real-life problem scenarios. The essential steps in problem solving typically involve:

• Understanding the Problem: Take the time to read and comprehend what is being asked in the problem. Check units and make sure to note any specific needs or constraints.
• Choosing a Strategy: Decide how you will approach solving the problem. In our exercise, subtraction is the key method since we want to find the difference between two values.
• Execution: Carry out the chosen plan. This might involve calculations, creating diagrams, or using formulas. Accuracy is vital, so double-check every step.
• Verification: After solving, always check if the result makes sense logically and mathematically. In this exercise, after finding that the difference is 1030 feet, one should verify if this logically fits with the given elevations.

Learning and practicing these steps can significantly improve one's ability to solve a variety of problems systematically and effectively.