The sum of two numbers is 345678. If one number is sixteen thousand sixteen greater than the other number, what is the greatest number?

Options

A. 164831
B. 170847
C. 180847
D. 329662

Answer

To solve the problem step by step, let's define the two numbers based on the information given:

1. **Let the first number be \( x \)**.
2. **The second number will then be \( 345678 - x \)** since the sum of the two numbers is 345678.

Now, according to the problem, we know that:

3. **The second number is 16,016 greater than the first number**. This can be expressed as:
\[ 345678 - x = x + 16016 \]

4. **Now, we can rearrange this equation**. First, we will add \( x \) to both sides:
\[ 345678 = 2x + 16016 \]

5. **Next, we will subtract 16,016 from both sides**:
\[ 345678 - 16016 = 2x \]
\[ 329662 = 2x \]

6. **Now, we will divide both sides by 2 to solve for \( x \)**:
\[ x = \frac{329662}{2} = 164831 \]

7. **Now that we have \( x \), we can find the second number**:
\[ 345678 - x = 345678 - 164831 = 180847 \]

8. **Finally, we determine which number is greater**. The two numbers are:
- First number: \( 164831 \)
- Second number: \( 180847 \)

Thus, the greatest number is **180847**.