Understanding the Problem: Sum of Resulting Numbers

The question asks us to find the sum of resulting numbers when a specific operation is performed on the number 100 using a whole number.

We are given a whole number. Let's call this whole number 'x'. A whole number is any non-negative integer (0, 1, 2, 3, ...).

According to the problem, two steps are performed:

1. The whole number (x) is added to 100.
2. The same whole number (x) is subtracted from 100.

We need to find the sum of the two numbers obtained from these two steps. This is the sum of resulting numbers.

Step 1: Identify the Two Resulting Numbers

Let the chosen whole number be represented by the variable \(x\).

• When the whole number \(x\) is added to 100, the first resulting number is \(100 + x\).
• When the same whole number \(x\) is subtracted from 100, the second resulting number is \(100 - x\).

Step 2: Calculate the Sum of the Resulting Numbers

Now, we need to find the sum of these two resulting numbers:

Sum = (First resulting number) + (Second resulting number)

Sum = \((100 + x) + (100 - x)\)

Step 3: Simplify the Expression to Find the Sum

Let's simplify the expression for the sum:

Sum = \(100 + x + 100 - x\)

We can rearrange the terms:

Sum = \( (100 + 100) + (x - x) \)

Sum = \( 200 + 0 \)

Sum = \( 200 \)

Conclusion: The Sum of Resulting Numbers is Always 200

As we can see from the calculation, the sum of the two resulting numbers is always 200, regardless of which whole number \(x\) was chosen. The \(+x\) and \(-x\) terms cancel each other out.

Let's take an example:

• Suppose the whole number is 10.
  • Added to 100: \(100 + 10 = 110\)
  • Subtracted from 100: \(100 - 10 = 90\)
  • Sum of resulting numbers: \(110 + 90 = 200\)
• Suppose the whole number is 55.
  • Added to 100: \(100 + 55 = 155\)
  • Subtracted from 100: \(100 - 55 = 45\)
  • Sum of resulting numbers: \(155 + 45 = 200\)

In both examples, the sum of resulting numbers is 200. This confirms our algebraic result.

Therefore, the sum of the two resulting numbers so obtained is 200.