A whole number is added to 50 and the same number is subtracted from 50. The sum of the resulting numbers is

Question

Accepted Answer

To solve the problem, let's break down the operations described in the question:

1. A whole number, let's call it $ x $, is added to 50. This gives us the expression $ 50 + x $.
2. The same number $ x $ is subtracted from 50. This gives us the expression $ 50 - x $.

The question asks for the sum of the resulting numbers from these two operations. Therefore, we need to calculate:

$$
(50 + x) + (50 - x)
$$

Simplifying this expression:

$$
50 + x + 50 - x = 50 + 50 + x - x = 100
$$

Thus, the sum of the resulting numbers is 100.

Now, let's justify why Option 4 is correct and why the other options are incorrect:

1. **Option 1 (25):** This option is incorrect because the calculation clearly shows that the sum is 100, not 25. There is no operation in the problem that would result in a sum of 25.

2. **Option 2 (50):** This option is incorrect because the sum of the expressions $ 50 + x $ and $ 50 - x $ simplifies to 100, not 50. The presence of both $ +x $ and $-x$ ensures that they cancel each other out, leaving us with 100.

3. **Option 3 (0):** This option is incorrect because the sum of the expressions does not result in zero. The operations described in the problem lead to a sum of 100, as shown in the calculation.

4. **Option 4 (100):** This is the correct option because, as demonstrated, the sum of $ (50 + x) + (50 - x) $ simplifies to 100. The addition and subtraction of $ x $ cancel each other out, leaving the sum of the two 50s, which is 100.

Therefore, based on the logical and mathematical reasoning provided, Option 4 is indeed the correct answer.