91Ó°ÊÓ

The two tables show the heights of some selected mountains and the depths of some selected trenches. Use the information given to answer. \( \)\begin{array}{|l|c|}\hline \text { Mountain } & {\text { Height (in feet) }} \\\ {\text { Foraker }} & {17,400} \\ {\text { Wilson }} & {14,246} \\\ {\text { Pikes Peak }} & {14,110} \\ \hline\end{array} $$ \begin{array}{|l|c|}\hline\text {} & {\text { Depth }( \text { in feet } } \\ {\text { Trench }} & {\text { as a negative number }} \\ {\text { Philippine }} & {-32,995} \\ {\text { Cayman }} & {-24,721} \\ {\text { Java }} & {-23,376} \\ \hline \end{array} $$ How much deeper is the Philippine Trench than the Cayman Trench?

Step by step solution

01

Identify the Depths

First, find the depths of the Philippine Trench and the Cayman Trench from the table. For the Philippine Trench, the depth is given as \(-32,995\) feet, and for the Cayman Trench, it is given as \(-24,721\) feet.

02

Set Up the Equation

To find the difference in depth, set up the equation with the given values. The formula to find the difference between two numbers is: \( \text{Depth of Philippine Trench} - \text{Depth of Cayman Trench} \)

03

Substitute the Values

Substitute the given values into the equation: \( -32,995 - (-24,721) \)

04

Simplify the Equation

Simplify the equation by subtracting the depth of the Cayman Trench from the depth of the Philippine Trench. Remember, subtracting a negative number is the same as adding the positive equivalent: \( -32,995 + 24,721 \)

05

Calculate the Result

Perform the addition to find the difference: \( -32,995 + 24,721 = -8,274 \)

06

Interpret the Result

The result of \( -8,274 \) means that the Philippine Trench is 8,274 feet deeper than the Cayman Trench.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

difference calculation

To solve difference calculations, it’s crucial to understand the concept of subtraction applied over two numbers. Let's consider two depths: the Philippine Trench at \( -32,995 \) feet and the Cayman Trench at \( -24,721 \) feet.
We want to find out how much deeper the Philippine Trench is compared to the Cayman Trench. This is essentially about finding the difference between two values.
In mathematical terms, the difference calculation can be written as:
\[ \text{Difference} = \text{Depth of Philippine Trench} - \text{Depth of Cayman Trench} \]
For our example, substituting the values into the difference equation, we get:
\[ -32,995 - (-24,721) \]

negative numbers

Dealing with negative numbers can seem tricky, but it’s easier once you know the rules. Here, both trenches' depths are given as negative numbers because they are below sea level. So, the depths of \( -32,995 \) feet for the Philippine Trench and \( -24,721 \) feet for the Cayman Trench are both negative.
When subtracting a negative number from another, like in our equation \( -32,995 - (-24,721) \), it's crucial to remember that subtracting a negative value is the same as adding its positive equivalent:
\[ -32,995 + 24,721 \]
This principle allows for the simplification of expressions involving negative numbers, turning them into more familiar addition problems.

step-by-step solution

Let's walk through the solution step-by-step to thoroughly understand the process of calculating the difference in depths.

• Step 1: Identify the Depths
  Locate the depths in the table: -32,995 feet for the Philippine Trench and -24,721 feet for the Cayman Trench.
• Step 2: Set Up the Equation
  We’ll use the equation \[ \text{Depth of Philippine Trench} - \text{Depth of Cayman Trench} \], which can be written as \[ -32,995 - (-24,721) \]
• Step 3: Substitute the Values
  Substitute in the specific depths from the table: \[ -32,995 - (-24,721) \]
• Step 4: Simplify the Equation
  Convert the subtraction of a negative to an addition: \[ -32,995 + 24,721 \]
• Step 5: Calculate the Result
  Perform the addition: \[ -32,995 + 24,721 = -8,274 \]
• Step 6: Interpret the Result
  The answer, \( -8,274 \), tells us that the Philippine Trench is 8,274 feet deeper than the Cayman Trench.