Understanding the Sum of Resulting Numbers

Let's solve this problem about adding and subtracting a whole number from 25. We need to find the total when you add the result of adding a whole number to 25 and the result of subtracting the same whole number from 25.

This is a basic algebra problem, but we can also think of it using examples.

Representing the Numbers

Suppose the whole number is represented by the variable $x$. This $x$ can be any non-negative integer (0, 1, 2, 3, and so on).

• The first number we get is 25 plus the whole number, which is $25 + x$.
• The second number we get is 25 minus the same whole number, which is $25 - x$.

Calculating the Sum of the Resulting Numbers

Now, we add these two numbers together to find their sum. The sum of the resulting numbers is:

$(25 + x) + (25 - x)$

Let's perform the addition. We can remove the parentheses:

$25 + x + 25 - x$

We can rearrange and group the terms:

$(25 + 25) + (x - x)$

The terms $x$ and $-x$ cancel each other out, as $x - x = 0$.

$25 + 25 + 0$

Adding the remaining numbers:

$50$

So, the sum of the resulting numbers is 50.

Illustration with a Table

Here is a table showing the process:

Conclusion on the Sum of Resulting Numbers

As shown by the calculation and the table, when you add a whole number to 25 and subtract the same whole number from 25, the sum of the two numbers you get is always 50. The value of the whole number does not change the final sum of resulting numbers.