Question
On Odd Street, the house numbers are consecutive odd numbers. The sum of two neighbor house numbers is 5056 . What are the two house numbers for these neighbors?
Ask by Mccarthy Bob. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The two house numbers are 2527 and 2529.
Solution
Let’s determine the two consecutive odd house numbers on Odd Street whose sum is 5056.
1. **Define the house numbers:**
- Let the first house number be \( n \).
- Since the house numbers are consecutive odd numbers, the next house number is \( n + 2 \).
2. **Set up the equation based on the sum:**
\[
n + (n + 2) = 5056
\]
3. **Simplify the equation:**
\[
2n + 2 = 5056
\]
\[
2n = 5056 - 2
\]
\[
2n = 5054
\]
\[
n = \frac{5054}{2}
\]
\[
n = 2527
\]
4. **Find the neighboring house number:**
\[
n + 2 = 2527 + 2 = 2529
\]
**Conclusion:**
The two consecutive odd house numbers are **2527** and **2529**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the two consecutive odd house numbers, let's denote the first house number as \( n \) (an odd number). The next consecutive odd house number would then be \( n + 2 \). The equation formed by their sum can be expressed as: \[ n + (n + 2) = 5056 \] This simplifies to: \[ 2n + 2 = 5056 \] Subtracting 2 from both sides gives: \[ 2n = 5054 \] Dividing both sides by 2 results in: \[ n = 2527 \] Thus, the two consecutive odd house numbers are: \[ 2527 \] and \[ 2529 \].
