College

Select the correct answer.

The sum of two consecutive numbers is 157. This equation, where [tex]n[/tex] is the first number, represents the situation: [tex]2n + 1 = 157[/tex].

What is the first number?

A. 77
B. 78
C. 79
D. 80

Answer :

To solve the problem of finding the first number when the sum of two consecutive numbers is 157, we can set up an equation. Let's break it down step-by-step:

1. Understanding Consecutive Numbers:
- If one number is [tex]\( n \)[/tex], the next consecutive number is [tex]\( n + 1 \)[/tex].

2. Setting Up the Equation:
- The sum of two consecutive numbers is given as 157. Therefore, we can write this as:
[tex]\[
n + (n + 1) = 157
\][/tex]

3. Simplify the Equation:
- Combine like terms:
[tex]\[
2n + 1 = 157
\][/tex]

4. Solve for [tex]\( n \)[/tex]:
- To isolate [tex]\( n \)[/tex], first subtract 1 from both sides of the equation:
[tex]\[
2n = 156
\][/tex]
- Then, divide both sides by 2:
[tex]\[
n = 78
\][/tex]

Therefore, the first number is 78. So, the correct answer is B. 78.