Problem 43 - Algebra 1

Question

Heidi Zimmer plans to climb the highest peak in each continent. She has already climbed summits in North America, Europe, Africa, and South America. Copy and complete the table. Convert \(h,\) the height in meters, to the height in feet by dividing each given value of \(h\) by \(0.3048 .\) The last column shows how much shorter each mountain is than Mt. Everest, which is 29,029 feet high. $$ \begin{array}{|l|c|c|c|} \hline \text { Mountain, Continent } & h & \frac{h}{0.3048} & 29,029-\frac{h}{0.3048} \\ \hline \text { Mt. McKinley, North America } & 6194 & ? & ? \\ \hline \text { Mt. Elbrus, Europe } & 5633 & ? & ? \\ \hline \text { Mt. Kilimanjaro, Africa } & 5963 & ? & ? \\ \hline \text { Mt. Aconcagua, South America } & 6959 & ? & ? \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The heights of the mountains in feet: Mt. McKinley = 20320 feet, Mt. Elbrus = 18481 feet, Mt. Kilimanjaro = 19574 feet, Mt. Aconcagua = 22841 feet. \nEach mountain is shorter than Mt. Everest by: Mt. McKinley 8909 feet, Mt. Elbrus 10748 feet, Mt. Kilimanjaro 9655 feet, Mt. Aconcagua 6388 feet.

Step 1 - Convert heights to feet

The height in feet can be calculated by dividing the height in meters (\(h\)) by 0.3048. Thus, the heights of the mountains in feet are as follows: \nMt. McKinley = \(6194/0.3048 = 20320\) feet, \nMt. Elbrus = \(5633/0.3048 = 18481\) feet, \nMt. Kilimanjaro = \(5963/0.3048 = 19574\) feet, \nMt. Aconcagua = \(6959/0.3048 = 22841\) feet.

Step 2 - Calculate how much shorter each mountain is than Mt. Everest

To calculate how much shorter each mountain is than Mt. Everest, subtract the converted height of each mountain from the height of Mt. Everest (29,029 feet). Thus, \nMt. McKinley is \(29229 - 20320 = 8909\) feet shorter than Mt.Everest, \nMt. Elbrus is \(29229 - 18481 = 10748\) feet shorter than Mt.Everest, \nMt. Kilimanjaro is \(29229 - 19574 = 9655\) feet shorter than Mt.Everest, \nMt. Aconcagua is \(29229 - 22841 = 6388\) feet shorter than Mt.Everest.

Key Concepts

Unit Conversion

Unit conversion is a process crucial in mathematics and science, allowing us to transform measurements from one unit to another while keeping their true value the same. In this problem, we need to convert the heights of mountains from meters to feet. The essential conversion factor here is 1 meter equals 0.3048 feet. To convert measurements from meters to feet, we divide the height in meters by this factor. For instance, if a mountain is 6194 meters tall, you compute its height in feet as follows: \[ \text{Height in feet} = \frac{6194}{0.3048} \approx 20320 \text{ feet} \]This method ensures consistency across measurements, making data universally understandable. Remember:

• Identify the appropriate conversion factor.
• Apply division to convert to feet.
• Ensure the accuracy of your conversion by verifying with known values.

This skill is crucial in many real-world applications.

Subtraction

Subtraction is a fundamental mathematical operation where you take one quantity away from another. It is not just about calculating the difference but understanding the relationship between two values.In this exercise, subtraction is used to determine how much shorter each mountain is compared to Mt. Everest. Suppose Mt. McKinley has been calculated to be 20,320 feet tall. To find out the difference in height between Mt. McKinley and Mt. Everest:\[ \text{Difference} = 29229 - 20320 = 8909 \text{ feet} \]This step-by-step subtraction process is instrumental in comparing data and drawing conclusions. Keep in mind:

• Align the numbers correctly by place value before subtracting.
• Keep track of any borrowed numbers, especially in larger calculations.
• Check your work to ensure accuracy.

Mastery of subtraction aids in solving complex problems efficiently.

Measurement in Mathematics

Measurement in mathematics involves the process of quantifying objects and phenomena. It uses units and tools to provide descriptive information about dimensions, volume, area, or mass. This problem focuses on the height of mountains, an example of spatial measurement. Conversion and comparison require understanding both the metric system (meters) and the imperial system (feet). Measurement allows for:

• Comparison between different objects.
• Problem-solving in real-world scenarios.
• Accurate depiction of size and scale.

Practical measurement skills include: understanding unit systems, converting between these systems, and interpreting the results within given contexts. Grasping these concepts enables students to effectively approach and solve diverse mathematical and real-life challenges.