Pregunta
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
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The two house numbers are 2527 and 2529.
Solución
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**.
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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 \[ 2529 \].
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